Tessero\Special

apply(string $name, mixed ...$args): mixed

Call a function by its SciPy/NumPy name: Special::apply('log_ndtr', $x).

agm(mixed $a, mixed $b, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Compute the arithmetic-geometric mean of `a` and `b`.

aiZeros(mixed $nt): mixed

First nt zeros of Ai and Ai' with the associated values (scipy.special.ai_zeros).

airy(mixed $z, ?array $out = null): array

Airy functions and their derivatives.

airye(mixed $z, ?array $out = null): array

Exponentially scaled Airy functions and their derivatives.

assocLaguerre(mixed $x, mixed $n, mixed $k, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Associated Laguerre polynomial L_n^k(x) (= eval_genlaguerre(n, k, x)).

bdtr(mixed $k, mixed $n, mixed $p, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Binomial distribution cumulative distribution function.

bdtrc(mixed $k, mixed $n, mixed $p, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Binomial distribution survival function.

bdtri(mixed $k, mixed $n, mixed $y, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse function to `bdtr` with respect to `p`.

bdtrik(mixed $y, mixed $n, mixed $p, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse function to `bdtr` with respect to `k`.

bdtrin(mixed $k, mixed $y, mixed $p, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse function to `bdtr` with respect to `n`.

bei(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Kelvin function bei.

beiZeros(mixed $nt): mixed

First nt positive zeros of the Kelvin function bei (scipy.special.bei_zeros).

beip(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Derivative of the Kelvin function bei.

beipZeros(mixed $nt): mixed

First nt positive zeros of the Kelvin derivative bei' (scipy.special.beip_zeros).

ber(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Kelvin function ber.

berZeros(mixed $nt): mixed

First nt positive zeros of the Kelvin function ber (scipy.special.ber_zeros).

bernoulli(mixed $n): mixed

The first n+1 Bernoulli numbers (scipy.special.bernoulli).

berp(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Derivative of the Kelvin function ber.

berpZeros(mixed $nt): mixed

First nt positive zeros of the Kelvin derivative ber' (scipy.special.berp_zeros).

besselpoly(mixed $a, mixed $lmb, mixed $nu, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Weighted integral of the Bessel function of the first kind.

beta(mixed $a, mixed $b, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Beta function.

betainc(mixed $a, mixed $b, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Regularized incomplete beta function.

betaincc(mixed $a, mixed $b, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Complement of the regularized incomplete beta function.

betainccinv(mixed $a, mixed $b, mixed $y, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse of the complemented regularized incomplete beta function.

betaincinv(mixed $a, mixed $b, mixed $y, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse of the regularized incomplete beta function.

betaln(mixed $a, mixed $b, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Natural logarithm of absolute value of beta function.

biZeros(mixed $nt): mixed

First nt zeros of Bi and Bi' with the associated values (scipy.special.bi_zeros).

binom(mixed $x, mixed $y, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Binomial coefficient considered as a function of two real variables.

boxcox(mixed $x, mixed $lmbda, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Compute the Box-Cox transformation.

boxcox1p(mixed $x, mixed $lmbda, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Compute the Box-Cox transformation of 1 + `x`.

btdtria(mixed $p, mixed $b, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse of `betainc` with respect to `a`.

btdtrib(mixed $x0, mixed $x1, mixed $x2, ?Tessero\NDArray $out = null): Tessero\NDArray|float

btdtria(a, p, x, out=None).

cRoots(mixed $n, mixed $mu = false): mixed

Alias of roots_chebyc (scipy.special.c_roots).

cbrt(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Element-wise cube root of `x`.

cgRoots(mixed $n, mixed $alpha, mixed $mu = false): mixed

Alias of roots_gegenbauer (scipy.special.cg_roots).

chdtr(mixed $v, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Chi square cumulative distribution function.

chdtrc(mixed $v, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Chi square survival function.

chdtri(mixed $v, mixed $p, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse to `chdtrc` with respect to `x`.

chdtriv(mixed $p, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse to `chdtr` with respect to `v`.

chndtr(mixed $x, mixed $df, mixed $nc, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Non-central chi square cumulative distribution function.

chndtridf(mixed $x, mixed $p, mixed $nc, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse to `chndtr` vs `df`.

chndtrinc(mixed $x, mixed $df, mixed $p, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse to `chndtr` vs `nc`.

chndtrix(mixed $p, mixed $df, mixed $nc, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse to `chndtr` vs `x`.

comb(mixed $N, mixed $k, ?Tessero\NDArray $out = null): Tessero\NDArray|float

The number of combinations of N things taken k at a time (scipy.special.comb, exact=False, repetition=False).

cosdg(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Cosine of the angle `x` given in degrees.

cosm1(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

cos(x) - 1 for use when `x` is near zero.

cotdg(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Cotangent of the angle `x` given in degrees.

dawsn(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Dawson's integral.

digamma(mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

The digamma function (alias of psi).

diric(mixed $x, mixed $n, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Periodic sinc (Dirichlet) function.

ellipHarm(mixed $h2, mixed $k2, mixed $n, mixed $p, mixed $s): mixed

Ellipsoidal harmonic (Lame function of the first kind) E^p_n(s) (scipy.special.ellip_harm).

ellipHarm2(mixed $h2, mixed $k2, mixed $n, mixed $p, mixed $s): mixed

Ellipsoidal harmonic of the second kind F^p_n(s) (scipy.special.ellip_harm_2).

ellipNormal(mixed $h2, mixed $k2, mixed $n, mixed $p): mixed

Normalization constant for ellipsoidal harmonics (scipy.special.ellip_normal).

ellipe(mixed $m, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Complete elliptic integral of the second kind.

ellipeinc(mixed $phi, mixed $m, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Incomplete elliptic integral of the second kind.

ellipj(mixed $u, mixed $m, ?array $out = null): array

Jacobi elliptic functions.

ellipk(mixed $m, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Complete elliptic integral of the first kind.

ellipkinc(mixed $phi, mixed $m, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Incomplete elliptic integral of the first kind.

ellipkm1(mixed $p, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Complete elliptic integral of the first kind around `m` = 1.

elliprc(mixed $x, mixed $y, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Degenerate symmetric elliptic integral.

elliprd(mixed $x, mixed $y, mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Symmetric elliptic integral of the second kind.

elliprf(mixed $x, mixed $y, mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Completely-symmetric elliptic integral of the first kind.

elliprg(mixed $x, mixed $y, mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Completely-symmetric elliptic integral of the second kind.

elliprj(mixed $x, mixed $y, mixed $z, mixed $p, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Symmetric elliptic integral of the third kind.

entr(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Elementwise function for computing entropy.

erf(mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Returns the error function of complex argument.

erfZeros(mixed $nt): mixed

First nt complex zeros of erf (scipy.special.erf_zeros).

erfc(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Complementary error function, ``1 - erf(x)``.

erfcinv(mixed $y, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse of the complementary error function.

erfcx(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Scaled complementary error function, ``exp(x**2) * erfc(x)``.

erfi(mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Imaginary error function, ``-i erf(i z)``.

erfinv(mixed $y, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse of the error function.

euler(mixed $n): mixed

The first n+1 Euler numbers (scipy.special.euler).

evalChebyc(mixed $n, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Evaluate Chebyshev polynomial of the first kind on [-2, 2] at a point.

evalChebys(mixed $n, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Evaluate Chebyshev polynomial of the second kind on [-2, 2] at a point.

evalChebyt(mixed $n, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Evaluate Chebyshev polynomial of the first kind at a point.

evalChebyu(mixed $n, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Evaluate Chebyshev polynomial of the second kind at a point.

evalGegenbauer(mixed $n, mixed $alpha, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Evaluate Gegenbauer polynomial at a point.

evalGenlaguerre(mixed $n, mixed $alpha, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Evaluate generalized Laguerre polynomial at a point.

evalHermite(mixed $n, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Evaluate physicist's Hermite polynomial at a point.

evalHermitenorm(mixed $n, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Evaluate probabilist's (normalized) Hermite polynomial at a point.

evalJacobi(mixed $n, mixed $alpha, mixed $beta, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Evaluate Jacobi polynomial at a point.

evalLaguerre(mixed $n, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Evaluate Laguerre polynomial at a point.

evalLegendre(mixed $n, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Evaluate Legendre polynomial at a point.

evalShChebyt(mixed $n, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Evaluate shifted Chebyshev polynomial of the first kind at a point.

evalShChebyu(mixed $n, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Evaluate shifted Chebyshev polynomial of the second kind at a point.

evalShJacobi(mixed $n, mixed $p, mixed $q, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Evaluate shifted Jacobi polynomial at a point.

evalShLegendre(mixed $n, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Evaluate shifted Legendre polynomial at a point.

exp1(mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Exponential integral E1.

exp10(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Compute ``10**x`` element-wise.

exp2(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Compute ``2**x`` element-wise.

expi(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Exponential integral Ei.

expit(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Expit (a.k.a. logistic sigmoid) ufunc for ndarrays.

expm1(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Compute ``exp(x) - 1``.

expn(mixed $n, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Generalized exponential integral En.

exprel(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Relative error exponential, ``(exp(x) - 1)/x``.

factorial(mixed $n, ?Tessero\NDArray $out = null): Tessero\NDArray|float

The factorial n! as gamma(n+1), 0 for n<0 (scipy.special.factorial, exact=False).

factorial2(mixed $n): mixed

Double factorial n!! (scipy.special.factorial2, exact=False).

factorialk(mixed $n, mixed $k): mixed

Order-k multifactorial (scipy.special.factorialk, exact=False).

fdtr(mixed $dfn, mixed $dfd, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

F cumulative distribution function.

fdtrc(mixed $dfn, mixed $dfd, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

F survival function.

fdtri(mixed $dfn, mixed $dfd, mixed $p, ?Tessero\NDArray $out = null): Tessero\NDArray|float

The `p`-th quantile of the F-distribution.

fdtridfd(mixed $dfn, mixed $p, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse to `fdtr` vs dfd.

fresnel(mixed $z, ?array $out = null): array

Fresnel integrals.

fresnelZeros(mixed $nt): mixed

First nt complex zeros of the Fresnel sine and cosine integrals (scipy.special.fresnel_zeros).

fresnelcZeros(mixed $nt): mixed

First nt complex zeros of the Fresnel cosine integral (scipy.special.fresnelc_zeros).

fresnelsZeros(mixed $nt): mixed

First nt complex zeros of the Fresnel sine integral (scipy.special.fresnels_zeros).

gamma(mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

gamma function.

gammainc(mixed $a, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Regularized lower incomplete gamma function.

gammaincc(mixed $a, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Regularized upper incomplete gamma function.

gammainccinv(mixed $a, mixed $y, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse of the regularized upper incomplete gamma function.

gammaincinv(mixed $a, mixed $y, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse to the regularized lower incomplete gamma function.

gammaln(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Logarithm of the absolute value of the gamma function.

gammasgn(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Sign of the gamma function.

gdtr(mixed $a, mixed $b, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Gamma distribution cumulative distribution function.

gdtrc(mixed $a, mixed $b, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Gamma distribution survival function.

gdtria(mixed $p, mixed $b, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse of `gdtr` vs a.

gdtrib(mixed $a, mixed $p, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse of `gdtr` vs b.

gdtrix(mixed $a, mixed $b, mixed $p, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse of `gdtr` vs x.

h1vp(mixed $v, mixed $z, mixed $n = 1): mixed

First derivative of the Hankel function of the first kind (scipy.special.h1vp).

h2vp(mixed $v, mixed $z, mixed $n = 1): mixed

First derivative of the Hankel function of the second kind (scipy.special.h2vp).

hRoots(mixed $n, mixed $mu = false): mixed

Alias of roots_hermite (scipy.special.h_roots).

hankel1(mixed $v, mixed $z): mixed

Hankel function of the first kind (scipy.special.hankel1).

hankel1e(mixed $v, mixed $z): mixed

Exponentially scaled Hankel function of the first kind (scipy.special.hankel1e).

hankel2(mixed $v, mixed $z): mixed

Hankel function of the second kind (scipy.special.hankel2).

hankel2e(mixed $v, mixed $z): mixed

Exponentially scaled Hankel function of the second kind (scipy.special.hankel2e).

heRoots(mixed $n, mixed $mu = false): mixed

Alias of roots_hermitenorm (scipy.special.he_roots).

huber(mixed $delta, mixed $r, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Huber loss function.

hyp0f1(mixed $v, mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Confluent hypergeometric limit function 0F1.

hyp1f1(mixed $a, mixed $b, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Confluent hypergeometric function 1F1.

hyp2f1(mixed $a, mixed $b, mixed $c, mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Gauss hypergeometric function 2F1(a, b; c; z).

hyperu(mixed $a, mixed $b, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Confluent hypergeometric function U.

i0(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Modified Bessel function of order 0.

i0e(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Exponentially scaled modified Bessel function of order 0.

i1(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Modified Bessel function of order 1.

i1e(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Exponentially scaled modified Bessel function of order 1.

invBoxcox(mixed $y, mixed $lmbda, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Compute the inverse of the Box-Cox transformation.

invBoxcox1p(mixed $y, mixed $lmbda, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Compute the inverse of the Box-Cox transformation.

it2i0k0(mixed $x, ?array $out = null): array

Integrals related to modified Bessel functions of order 0.

it2j0y0(mixed $x, ?array $out = null): array

Integrals related to Bessel functions of the first kind of order 0.

it2struve0(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Integral related to the Struve function of order 0.

itairy(mixed $x, ?array $out = null): array

Integrals of Airy functions.

iti0k0(mixed $x, ?array $out = null): array

Integrals of modified Bessel functions of order 0.

itj0y0(mixed $x, ?array $out = null): array

Integrals of Bessel functions of the first kind of order 0.

itmodstruve0(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Integral of the modified Struve function of order 0.

itstruve0(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Integral of the Struve function of order 0.

iv(mixed $v, mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Modified Bessel function of the first kind of real order.

ive(mixed $v, mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Exponentially scaled modified Bessel function of the first kind.

ivp(mixed $v, mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

First derivative of the modified Bessel function of the first kind (scipy.special.ivp, n=1).

j0(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Bessel function of the first kind of order 0.

j1(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Bessel function of the first kind of order 1.

jRoots(mixed $n, mixed $alpha, mixed $beta, mixed $mu = false): mixed

Alias of roots_jacobi (scipy.special.j_roots).

jn(mixed $n, mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Bessel function of the first kind of real order and complex argument (alias of jv).

jnZeros(mixed $n, mixed $nt): mixed

First nt positive zeros of the Bessel function Jn (scipy.special.jn_zeros).

jnjnpZeros(mixed $nt): mixed

First nt zeros of Jn and Jn' by magnitude with their order/rank/type (scipy.special.jnjnp_zeros).

jnpZeros(mixed $n, mixed $nt): mixed

First nt positive zeros of the Bessel derivative Jn' (scipy.special.jnp_zeros).

jnynZeros(mixed $n, mixed $nt): mixed

First nt zeros of Jn, Jn', Yn, Yn' (scipy.special.jnyn_zeros).

jsRoots(mixed $n, mixed $p1, mixed $q1, mixed $mu = false): mixed

Alias of roots_sh_jacobi (scipy.special.js_roots).

jv(mixed $v, mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Bessel function of the first kind of real order and complex argument.

jve(mixed $v, mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Exponentially scaled Bessel function of the first kind of order `v`.

jvp(mixed $v, mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

First derivative of the Bessel function of the first kind (scipy.special.jvp, n=1).

k0(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Modified Bessel function of the second kind of order 0, :math:`K_0`.

k0e(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Exponentially scaled modified Bessel function K of order 0.

k1(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Modified Bessel function of the second kind of order 1, :math:`K_1(x)`.

k1e(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Exponentially scaled modified Bessel function K of order 1.

kei(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Kelvin function kei.

keiZeros(mixed $nt): mixed

First nt positive zeros of the Kelvin function kei (scipy.special.kei_zeros).

keip(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Derivative of the Kelvin function kei.

keipZeros(mixed $nt): mixed

First nt positive zeros of the Kelvin derivative kei' (scipy.special.keip_zeros).

kelvin(mixed $x): mixed

Kelvin functions as complex pairs (scipy.special.kelvin).

kelvinZeros(mixed $nt): mixed

First nt zeros of all eight Kelvin functions (scipy.special.kelvin_zeros).

ker(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Kelvin function ker.

kerZeros(mixed $nt): mixed

First nt positive zeros of the Kelvin function ker (scipy.special.ker_zeros).

kerp(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Derivative of the Kelvin function ker.

kerpZeros(mixed $nt): mixed

First nt positive zeros of the Kelvin derivative ker' (scipy.special.kerp_zeros).

klDiv(mixed $x, mixed $y, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Elementwise function for computing Kullback-Leibler divergence.

kn(mixed $n, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Modified Bessel function of the second kind of integer order `n`.

kolmogi(mixed $p, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse Survival Function of Kolmogorov distribution.

kolmogorov(mixed $y, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Complementary cumulative distribution (Survival Function) function of Kolmogorov distribution.

kv(mixed $v, mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Modified Bessel function of the second kind of real order `v`.

kve(mixed $v, mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Exponentially scaled modified Bessel function of the second kind.

kvp(mixed $v, mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

First derivative of the modified Bessel function of the second kind (scipy.special.kvp, n=1).

lRoots(mixed $n, mixed $mu = false): mixed

Alias of roots_laguerre (scipy.special.l_roots).

laRoots(mixed $n, mixed $alpha, mixed $mu = false): mixed

Alias of roots_genlaguerre (scipy.special.la_roots).

lambertw(mixed $z, mixed $k = 0, mixed $tol = 1.0E-8): mixed

Lambert W function, branch k (scipy.special.lambertw).

lmbda(mixed $v, mixed $x): mixed

Lambda function L_v(x) and its derivative for a sequence of orders (scipy.special.lmbda).

log1p(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Calculates log(1 + x) for use when `x` is near zero.

logExpit(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Logarithm of the logistic sigmoid function.

logNdtr(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Logarithm of Gaussian cumulative distribution function.

logSoftmax(mixed $x, mixed $axis = null): mixed

log of softmax over an axis (scipy.special.log_softmax; real).

logWrightBessel(mixed $a, mixed $b, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Natural logarithm of Wright's generalized Bessel function, see `wright_bessel`. This function comes in handy in particular for large values of x.

loggamma(mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Principal branch of the logarithm of the gamma function.

logit(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Logit ufunc for ndarrays.

logsumexp(mixed $a, mixed $axis = null, mixed $keepdims = false): mixed

Stable log of the sum of exponentials over an axis (scipy.special.logsumexp; real a, no b/return_sign).

lpmv(mixed $m, mixed $v, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Associated Legendre function of integer order and real degree.

mathieuA(mixed $m, mixed $q, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Characteristic value of even Mathieu functions.

mathieuB(mixed $m, mixed $q, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Characteristic value of odd Mathieu functions.

mathieuCem(mixed $m, mixed $q, mixed $x, ?array $out = null): array

Even Mathieu function and its derivative.

mathieuEvenCoef(mixed $m, mixed $q): mixed

Fourier coefficients of the even Mathieu function ce_m (scipy.special.mathieu_even_coef).

mathieuModcem1(mixed $m, mixed $q, mixed $x, ?array $out = null): array

Even modified Mathieu function of the first kind and its derivative.

mathieuModcem2(mixed $m, mixed $q, mixed $x, ?array $out = null): array

Even modified Mathieu function of the second kind and its derivative.

mathieuModsem1(mixed $m, mixed $q, mixed $x, ?array $out = null): array

Odd modified Mathieu function of the first kind and its derivative.

mathieuModsem2(mixed $m, mixed $q, mixed $x, ?array $out = null): array

Odd modified Mathieu function of the second kind and its derivative.

mathieuOddCoef(mixed $m, mixed $q): mixed

Fourier coefficients of the odd Mathieu function se_m (scipy.special.mathieu_odd_coef).

mathieuSem(mixed $m, mixed $q, mixed $x, ?array $out = null): array

Odd Mathieu function and its derivative.

modfresnelm(mixed $x): mixed

Modified Fresnel negative integrals F-(x) and K-(x) (scipy.special.modfresnelm).

modfresnelp(mixed $x): mixed

Modified Fresnel positive integrals F+(x) and K+(x) (scipy.special.modfresnelp).

modstruve(mixed $v, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Modified Struve function.

multigammaln(mixed $a, mixed $d): mixed

Log of the multivariate gamma function (scipy.special.multigammaln).

nbdtr(mixed $k, mixed $n, mixed $p, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Negative binomial cumulative distribution function.

nbdtrc(mixed $k, mixed $n, mixed $p, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Negative binomial survival function.

nbdtri(mixed $k, mixed $n, mixed $y, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Returns the inverse with respect to the parameter `p` of ``y = nbdtr(k, n, p)``, the negative binomial cumulative distribution function.

nbdtrik(mixed $y, mixed $n, mixed $p, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Negative binomial percentile function.

nbdtrin(mixed $k, mixed $y, mixed $p, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse of `nbdtr` vs `n`.

ncfdtr(mixed $dfn, mixed $dfd, mixed $nc, mixed $f, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Cumulative distribution function of the non-central F distribution.

ncfdtri(mixed $dfn, mixed $dfd, mixed $nc, mixed $p, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse with respect to `f` of the CDF of the non-central F distribution.

ncfdtridfd(mixed $dfn, mixed $p, mixed $nc, mixed $f, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Calculate degrees of freedom (denominator) for the noncentral F-distribution.

ncfdtridfn(mixed $p, mixed $dfd, mixed $nc, mixed $f, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Calculate degrees of freedom (numerator) for the noncentral F-distribution.

ncfdtrinc(mixed $dfn, mixed $dfd, mixed $p, mixed $f, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Calculate non-centrality parameter for non-central F distribution.

nctdtr(mixed $df, mixed $nc, mixed $t, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Cumulative distribution function of the non-central `t` distribution.

nctdtridf(mixed $p, mixed $nc, mixed $t, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Calculate degrees of freedom for non-central t distribution.

nctdtrinc(mixed $df, mixed $p, mixed $t, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Calculate non-centrality parameter for non-central t distribution.

nctdtrit(mixed $df, mixed $nc, mixed $p, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse cumulative distribution function of the non-central t distribution.

ndtr(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Cumulative distribution of the standard normal distribution.

ndtri(mixed $y, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse of `ndtr` vs x.

ndtriExp(mixed $y, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse of `log_ndtr` vs x. Allows for greater precision than `ndtri` composed with `numpy.exp` for very small values of y and for y close to 0.

nrdtrimn(mixed $p, mixed $std, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Calculate mean of normal distribution given other params.

nrdtrisd(mixed $mn, mixed $p, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Calculate standard deviation of normal distribution given other params.

oblAng1(mixed $m, mixed $n, mixed $c, mixed $x, ?array $out = null): array

Oblate spheroidal angular function of the first kind and its derivative.

oblAng1Cv(mixed $m, mixed $n, mixed $c, mixed $cv, mixed $x, ?array $out = null): array

Oblate spheroidal angular function obl_ang1 for precomputed characteristic value.

oblCv(mixed $m, mixed $n, mixed $c, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Characteristic value of oblate spheroidal function.

oblCvSeq(mixed $m, mixed $n, mixed $c): mixed

Oblate spheroidal characteristic values for modes m..n (scipy.special.obl_cv_seq).

oblRad1(mixed $m, mixed $n, mixed $c, mixed $x, ?array $out = null): array

Oblate spheroidal radial function of the first kind and its derivative.

oblRad1Cv(mixed $m, mixed $n, mixed $c, mixed $cv, mixed $x, ?array $out = null): array

Oblate spheroidal radial function obl_rad1 for precomputed characteristic value.

oblRad2(mixed $m, mixed $n, mixed $c, mixed $x, ?array $out = null): array

Oblate spheroidal radial function of the second kind and its derivative.

oblRad2Cv(mixed $m, mixed $n, mixed $c, mixed $cv, mixed $x, ?array $out = null): array

Oblate spheroidal radial function obl_rad2 for precomputed characteristic value.

owensT(mixed $h, mixed $a, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Owen's T Function.

pRoots(mixed $n, mixed $mu = false): mixed

Alias of roots_legendre (scipy.special.p_roots).

pbdnSeq(mixed $n, mixed $z): mixed

Complex parabolic cylinder Dn(z) and derivatives for a sequence of orders (scipy.special.pbdn_seq).

pbdv(mixed $v, mixed $x, ?array $out = null): array

Parabolic cylinder function D.

pbdvSeq(mixed $v, mixed $x): mixed

Parabolic cylinder Dv(x) and derivatives for a sequence of orders (scipy.special.pbdv_seq).

pbvv(mixed $v, mixed $x, ?array $out = null): array

Parabolic cylinder function V.

pbvvSeq(mixed $v, mixed $x): mixed

Parabolic cylinder Vv(x) and derivatives for a sequence of orders (scipy.special.pbvv_seq).

pbwa(mixed $a, mixed $x, ?array $out = null): array

Parabolic cylinder function W.

pdtr(mixed $k, mixed $m, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Poisson cumulative distribution function.

pdtrc(mixed $k, mixed $m, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Poisson survival function.

pdtri(mixed $k, mixed $y, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse to `pdtr` vs m.

pdtrik(mixed $p, mixed $m, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse to `pdtr` vs `k`.

perm(mixed $N, mixed $k, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Number of permutations of N things taken k at a time (non-exact, via the Pochhammer symbol).

poch(mixed $z, mixed $m, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Pochhammer symbol.

polygamma(mixed $n, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Polygamma function of order n: the (n+1)-th derivative of the logarithm of the gamma function (scipy.special.polygamma).

powm1(mixed $x, mixed $y, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Computes ``x**y - 1``.

proAng1(mixed $m, mixed $n, mixed $c, mixed $x, ?array $out = null): array

Prolate spheroidal angular function of the first kind and its derivative.

proAng1Cv(mixed $m, mixed $n, mixed $c, mixed $cv, mixed $x, ?array $out = null): array

Prolate spheroidal angular function pro_ang1 for precomputed characteristic value.

proCv(mixed $m, mixed $n, mixed $c, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Characteristic value of prolate spheroidal function.

proCvSeq(mixed $m, mixed $n, mixed $c): mixed

Prolate spheroidal characteristic values for modes m..n (scipy.special.pro_cv_seq).

proRad1(mixed $m, mixed $n, mixed $c, mixed $x, ?array $out = null): array

Prolate spheroidal radial function of the first kind and its derivative.

proRad1Cv(mixed $m, mixed $n, mixed $c, mixed $cv, mixed $x, ?array $out = null): array

Prolate spheroidal radial function pro_rad1 for precomputed characteristic value.

proRad2(mixed $m, mixed $n, mixed $c, mixed $x, ?array $out = null): array

Prolate spheroidal radial function of the second kind and its derivative.

proRad2Cv(mixed $m, mixed $n, mixed $c, mixed $cv, mixed $x, ?array $out = null): array

Prolate spheroidal radial function pro_rad2 for precomputed characteristic value.

psRoots(mixed $n, mixed $mu = false): mixed

Alias of roots_sh_legendre (scipy.special.ps_roots).

pseudoHuber(mixed $delta, mixed $r, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Pseudo-Huber loss function.

psi(mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

The digamma function.

radian(mixed $d, mixed $m, mixed $s, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Convert from degrees to radians.

relEntr(mixed $x, mixed $y, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Elementwise function for computing relative entropy.

rgamma(mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Reciprocal of the gamma function.

rootsChebyc(mixed $n, mixed $mu = false): mixed

Gauss-Chebyshev 1st-kind quadrature on [-2, 2] (scipy.special.roots_chebyc).

rootsChebys(mixed $n, mixed $mu = false): mixed

Gauss-Chebyshev 2nd-kind quadrature on [-2, 2] (scipy.special.roots_chebys).

rootsChebyt(mixed $n, mixed $mu = false): mixed

Gauss-Chebyshev 1st-kind quadrature (scipy.special.roots_chebyt).

rootsChebyu(mixed $n, mixed $mu = false): mixed

Gauss-Chebyshev 2nd-kind quadrature (scipy.special.roots_chebyu).

rootsGegenbauer(mixed $n, mixed $alpha, mixed $mu = false): mixed

Gauss-Gegenbauer quadrature (scipy.special.roots_gegenbauer).

rootsGenlaguerre(mixed $n, mixed $alpha, mixed $mu = false): mixed

generalized Gauss-Laguerre quadrature (scipy.special.roots_genlaguerre).

rootsHermite(mixed $n, mixed $mu = false): mixed

Gauss-Hermite (physicists) quadrature (scipy.special.roots_hermite).

rootsHermitenorm(mixed $n, mixed $mu = false): mixed

Gauss-Hermite (probabilists) quadrature (scipy.special.roots_hermitenorm).

rootsJacobi(mixed $n, mixed $alpha, mixed $beta, mixed $mu = false): mixed

Gauss-Jacobi quadrature (scipy.special.roots_jacobi).

rootsLaguerre(mixed $n, mixed $mu = false): mixed

Gauss-Laguerre quadrature (scipy.special.roots_laguerre).

rootsLegendre(mixed $n, mixed $mu = false): mixed

Gauss-Legendre quadrature (scipy.special.roots_legendre).

rootsShChebyt(mixed $n, mixed $mu = false): mixed

Shifted Gauss-Chebyshev 1st-kind quadrature on [0, 1] (scipy.special.roots_sh_chebyt).

rootsShChebyu(mixed $n, mixed $mu = false): mixed

Shifted Gauss-Chebyshev 2nd-kind quadrature on [0, 1] (scipy.special.roots_sh_chebyu).

rootsShJacobi(mixed $n, mixed $p1, mixed $q1, mixed $mu = false): mixed

shifted Gauss-Jacobi on [0, 1] quadrature (scipy.special.roots_sh_jacobi).

rootsShLegendre(mixed $n, mixed $mu = false): mixed

shifted Gauss-Legendre on [0, 1] quadrature (scipy.special.roots_sh_legendre).

round(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Round to the nearest integer.

sRoots(mixed $n, mixed $mu = false): mixed

Alias of roots_chebys (scipy.special.s_roots).

shichi(mixed $x, ?array $out = null): array

Hyperbolic sine and cosine integrals.

sici(mixed $x, ?array $out = null): array

Sine and cosine integrals.

sinc(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Normalized sinc, sin(pi x)/(pi x) with sinc(0)=1 (scipy.special.sinc).

sindg(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Sine of the angle `x` given in degrees.

smirnov(mixed $n, mixed $d, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Kolmogorov-Smirnov complementary cumulative distribution function.

smirnovi(mixed $n, mixed $p, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse to `smirnov`.

softmax(mixed $x, mixed $axis = null): mixed

exp(x) normalised over an axis (scipy.special.softmax; real).

softplus(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Softplus, log(1 + exp(x)), evaluated stably (scipy.special.softplus).

spence(mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Spence's function, also known as the dilogarithm.

sphHarmY(mixed $n, mixed $m, mixed $theta, mixed $phi): mixed

Spherical harmonic Y_n^m (scipy.special.sph_harm_y).

sphericalIn(mixed $n, mixed $z, mixed $derivative, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Modified spherical Bessel function of the first kind, or its derivative (scipy.special.spherical_in).

sphericalJn(mixed $n, mixed $z, mixed $derivative, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Spherical Bessel function of the first kind, or its derivative (scipy.special.spherical_jn).

sphericalKn(mixed $n, mixed $z, mixed $derivative, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Modified spherical Bessel function of the second kind, or its derivative (scipy.special.spherical_kn).

sphericalYn(mixed $n, mixed $z, mixed $derivative, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Spherical Bessel function of the second kind, or its derivative (scipy.special.spherical_yn).

stdtr(mixed $df, mixed $t, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Student t distribution cumulative distribution function.

stdtridf(mixed $p, mixed $t, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Inverse of `stdtr` vs df.

stdtrit(mixed $df, mixed $p, ?Tessero\NDArray $out = null): Tessero\NDArray|float

The `p`-th quantile of the student t distribution.

struve(mixed $v, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Struve function.

tRoots(mixed $n, mixed $mu = false): mixed

Alias of roots_chebyt (scipy.special.t_roots).

tandg(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Tangent of angle `x` given in degrees.

tklmbda(mixed $x, mixed $lmbda, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Cumulative distribution function of the Tukey lambda distribution.

tsRoots(mixed $n, mixed $mu = false): mixed

Alias of roots_sh_chebyt (scipy.special.ts_roots).

uRoots(mixed $n, mixed $mu = false): mixed

Alias of roots_chebyu (scipy.special.u_roots).

usRoots(mixed $n, mixed $mu = false): mixed

Alias of roots_sh_chebyu (scipy.special.us_roots).

voigtProfile(mixed $x, mixed $sigma, mixed $gamma, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Voigt profile.

wofz(mixed $z): mixed

Faddeeva function w(z) = exp(-z^2) erfc(-iz) (scipy.special.wofz).

wrightBessel(mixed $a, mixed $b, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Wright's generalized Bessel function.

wrightomega(mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Wright Omega function.

xlog1py(mixed $x, mixed $y, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Compute ``x*log1p(y)`` so that the result is 0 if ``x = 0``.

xlogy(mixed $x, mixed $y, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Compute ``x*log(y)`` so that the result is 0 if ``x = 0``.

y0(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Bessel function of the second kind of order 0.

y0Zeros(mixed $nt): mixed

First nt zeros of Y0 and the value of Y0' there (scipy.special.y0_zeros).

y1(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Bessel function of the second kind of order 1.

y1Zeros(mixed $nt): mixed

First nt zeros of Y1 and the value of Y1' there (scipy.special.y1_zeros).

y1pZeros(mixed $nt): mixed

First nt zeros of Y1' and the value of Y1 there (scipy.special.y1p_zeros).

yn(mixed $n, mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Bessel function of the second kind of integer order and real argument.

ynZeros(mixed $n, mixed $nt): mixed

First nt positive zeros of the Bessel function Yn (scipy.special.yn_zeros).

ynpZeros(mixed $n, mixed $nt): mixed

First nt positive zeros of the Bessel derivative Yn' (scipy.special.ynp_zeros).

yv(mixed $v, mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Bessel function of the second kind of real order and complex argument.

yve(mixed $v, mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Exponentially scaled Bessel function of the second kind of real order.

yvp(mixed $v, mixed $z, ?Tessero\NDArray $out = null): Tessero\NDArray|float

First derivative of the Bessel function of the second kind (scipy.special.yvp, n=1).

zeta(mixed $x, mixed $q, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Hurwitz zeta function (scipy.special.zeta).

zetac(mixed $x, ?Tessero\NDArray $out = null): Tessero\NDArray|float

Riemann zeta function minus 1.