# Special Functions#

## Airy functions#

 `mars.tensor.special.airy` Airy functions and their derivatives. `mars.tensor.special.airye` Exponentially scaled Airy functions and their derivatives. `mars.tensor.special.itairy` Integrals of Airy functions

## Information Theory functions#

 `mars.tensor.special.entr` Elementwise function for computing entropy. `mars.tensor.special.rel_entr` Elementwise function for computing relative entropy.

## Bessel functions#

 `mars.tensor.special.jv` Bessel function of the first kind of real order and complex argument. `mars.tensor.special.jve` Exponentially scaled Bessel function of order v. `mars.tensor.special.yn` Bessel function of the second kind of integer order and real argument. `mars.tensor.special.yv` Bessel function of the second kind of real order and complex argument. `mars.tensor.special.yve` Exponentially scaled Bessel function of the second kind of real order. `mars.tensor.special.kn` Modified Bessel function of the second kind of integer order n `mars.tensor.special.kv` Modified Bessel function of the second kind of real order v `mars.tensor.special.kve` Exponentially scaled modified Bessel function of the second kind. `mars.tensor.special.iv` Modified Bessel function of the first kind of real order. `mars.tensor.special.ive` Exponentially scaled modified Bessel function of the first kind `mars.tensor.special.hankel1` Hankel function of the first kind `mars.tensor.special.hankel1e` Exponentially scaled Hankel function of the first kind `mars.tensor.special.hankel2` Hankel function of the second kind `mars.tensor.special.hankel2e` Exponentially scaled Hankel function of the second kind

## Error functions and fresnel integrals#

 `mars.tensor.special.erf` Returns the error function of complex argument. `mars.tensor.special.erfc` Complementary error function, `1 - erf(x)`. `mars.tensor.special.erfcx` Scaled complementary error function, `exp(x**2) * erfc(x)`. `mars.tensor.special.erfi` Imaginary error function, `-i erf(i z)`. `mars.tensor.special.erfinv` Inverse of the error function. `mars.tensor.special.erfcinv` Inverse of the complementary error function. `mars.tensor.special.wofz` Faddeeva function `mars.tensor.special.dawsn` Dawson's integral. `mars.tensor.special.fresnel` Fresnel integrals. `mars.tensor.special.modfresnelp` Modified Fresnel positive integrals `mars.tensor.special.modfresnelm` Modified Fresnel negative integrals

## Ellipsoidal harmonics#

 `mars.tensor.special.ellip_harm` Ellipsoidal harmonic functions E^p_n(l) `mars.tensor.special.ellip_harm_2` Ellipsoidal harmonic functions F^p_n(l) `mars.tensor.special.ellip_normal` Ellipsoidal harmonic normalization constants gamma^p_n

## Elliptic functions and integrals#

 `mars.tensor.special.ellipk` Complete elliptic integral of the first kind. `mars.tensor.special.ellipkm1` Complete elliptic integral of the first kind around m = 1 `mars.tensor.special.ellipkinc` Incomplete elliptic integral of the first kind `mars.tensor.special.ellipe` Complete elliptic integral of the second kind `mars.tensor.special.ellipeinc` Incomplete elliptic integral of the second kind

## Convenience functions#

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