# Special functions (cupyx.scipy.special)¶

## Bessel functions¶

 j0 Bessel function of the first kind of order 0. j1 Bessel function of the first kind of order 1. y0 Bessel function of the second kind of order 0. y1 Bessel function of the second kind of order 1. yn Bessel function of the second kind of order n. i0 Modified Bessel function of order 0. i0e Exponentially scaled modified Bessel function of order 0. i1 Modified Bessel function of order 1. i1e Exponentially scaled modified Bessel function of order 1.

## Raw statistical functions¶

 bdtr Binomial distribution cumulative distribution function. bdtrc Binomial distribution survival function. bdtri Inverse function to bdtr with respect to p. btdtr Cumulative distribution function of the beta distribution. btdtri The p-th quantile of the beta distribution. fdtr F cumulative distribution function. fdtrc F survival function. fdtri The p-th quantile of the F-distribution. gdtr Gamma distribution cumulative distribution function. gdtrc Gamma distribution survival function. nbdtr Negative binomial distribution cumulative distribution function. nbdtrc Negative binomial distribution survival function. nbdtri Inverse function to nbdtr with respect to p. pdtr Poisson cumulative distribution function. pdtrc Binomial distribution survival function. pdtri Inverse function to pdtr with respect to m. chdtr Chi-square cumulative distribution function. chdtrc Chi square survival function. chdtri Inverse to chdtrc with respect to x. ndtr Cumulative distribution function of normal distribution. log_ndtr Logarithm of Gaussian cumulative distribution function. ndtri Inverse of the cumulative distribution function of the standard logit Logit function. expit Logistic sigmoid function (expit). log_expit Logarithm of the logistic sigmoid function. boxcox Compute the Box-Cox transformation. boxcox1p Compute the Box-Cox transformation op 1 + x. inv_boxcox Compute the Box-Cox transformation. inv_boxcox1p Compute the Box-Cox transformation op 1 + x.

## Information Theory functions¶

 entr Elementwise function for computing entropy. rel_entr Elementwise function for computing relative entropy. kl_div Elementwise function for computing Kullback-Leibler divergence. huber Elementwise function for computing the Huber loss. pseudo_huber Elementwise function for computing the Pseudo-Huber loss.

## Error function and Fresnel integrals¶

 erf Error function. erfc Complementary error function. erfcx Scaled complementary error function. erfinv Inverse function of error function. erfcinv Inverse function of complementary error function.

## Legendre functions¶

 lpmv Associated Legendre function of integer order and real degree. sph_harm Spherical Harmonic.

## Other special functions¶

 expn Generalized exponential integral En. zeta Hurwitz zeta function.

## Convenience functions¶

 cbrt Cube root. exp10 Computes 10**x. exp2 Computes 2**x. radian Degrees, minutes, seconds to radians: cosdg Cosine of x with x in degrees. sindg Sine of x with x in degrees. tandg Tangent of x with x in degrees. cotdg Cotangent of x with x in degrees. log1p Elementwise function for scipy.special.log1p expm1 Computes exp(x) - 1. round(a[, decimals, out]) xlogy Compute x*log(y) so that the result is 0 if x = 0. xlog1py Compute x*log1p(y) so that the result is 0 if x = 0. sinc Elementwise sinc function.