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

Gamma and related functions

mars.tensor.special.gamma	gamma function.
mars.tensor.special.gammaln	Logarithm of the absolute value of the Gamma function.
mars.tensor.special.loggamma	Principal branch of the logarithm of the gamma function.
mars.tensor.special.gammasgn	Sign of the gamma function.
mars.tensor.special.gammainc	Regularized lower incomplete gamma function.
mars.tensor.special.gammaincinv	Inverse to the lower incomplete gamma function with respect to x.
mars.tensor.special.gammaincc	Regularized lower incomplete gamma function.
mars.tensor.special.gammainccinv	Inverse of the upper incomplete gamma function with respect to x
mars.tensor.special.beta	Beta function.
mars.tensor.special.betaln	Natural logarithm of absolute value of beta function.
mars.tensor.special.betainc	Incomplete beta function.
mars.tensor.special.betaincinv	Inverse of the incomplete beta function.
mars.tensor.special.psi	The digamma function.
mars.tensor.special.rgamma	Reciprocal of the gamma function.
mars.tensor.special.polygamma	Polygamma functions.
mars.tensor.special.multigammaln	Returns the log of multivariate gamma, also sometimes called the generalized gamma.
mars.tensor.special.digamma	The digamma function.
mars.tensor.special.poch	Pochhammer symbol.

Convenience functions

mars.tensor.special.xlogy

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