# 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. `log_softmax`(x[, axis]) Compute logarithm of softmax function `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.