Special Functions

Airy functions

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

Information Theory functions

maxframe.tensor.special.entr	Elementwise function for computing entropy.
maxframe.tensor.special.rel_entr	Elementwise function for computing relative entropy.

Bessel functions

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

Error functions and fresnel integrals

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

Ellipsoidal harmonics

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

Elliptic functions and integrals

maxframe.tensor.special.ellipk	Complete elliptic integral of the first kind.
maxframe.tensor.special.ellipkm1	Complete elliptic integral of the first kind around m = 1
maxframe.tensor.special.ellipkinc	Incomplete elliptic integral of the first kind
maxframe.tensor.special.ellipe	Complete elliptic integral of the second kind
maxframe.tensor.special.ellipeinc	Incomplete elliptic integral of the second kind
maxframe.tensor.special.elliprc	Degenerate symmetric elliptic integral.
maxframe.tensor.special.elliprf	Completely-symmetric elliptic integral of the first kind.
maxframe.tensor.special.elliprg	Completely-symmetric elliptic integral of the second kind.
maxframe.tensor.special.elliprj	Symmetric elliptic integral of the third kind.

Gamma and related functions

maxframe.tensor.special.gamma	gamma function.
maxframe.tensor.special.gammaln	Logarithm of the absolute value of the Gamma function.
maxframe.tensor.special.loggamma	Principal branch of the logarithm of the gamma function.
maxframe.tensor.special.gammasgn	Sign of the gamma function.
maxframe.tensor.special.gammainc	Regularized lower incomplete gamma function.
maxframe.tensor.special.gammaincinv	Inverse to the regularized lower incomplete gamma function.
maxframe.tensor.special.gammaincc	gammainc(a, x, out=None)
maxframe.tensor.special.gammainccinv	Inverse of the regularized upper incomplete gamma function.
maxframe.tensor.special.beta	Beta function.
maxframe.tensor.special.betaln	Natural logarithm of absolute value of beta function.
maxframe.tensor.special.betainc	Regularized incomplete beta function.
maxframe.tensor.special.betaincinv	Inverse of the regularized incomplete beta function.
maxframe.tensor.special.psi	The digamma function.
maxframe.tensor.special.rgamma	Reciprocal of the gamma function.
maxframe.tensor.special.polygamma	Polygamma functions.
maxframe.tensor.special.multigammaln	Returns the log of multivariate gamma, also sometimes called the generalized gamma.
maxframe.tensor.special.digamma	psi(z, out=None)
maxframe.tensor.special.poch	Pochhammer symbol.

Sigmoidal functions

maxframe.tensor.special.expit	Expit (a.k.a.
maxframe.tensor.special.log_expit	Logarithm of the logistic sigmoid function.
maxframe.tensor.special.logit	Logit ufunc for ndarrays.

Other special functions

maxframe.tensor.special.softmax	Compute the softmax function. The softmax function transforms each element of a collection by computing the exponential of each element divided by the sum of the exponentials of all the elements. That is, if x is a one-dimensional numpy array::.
maxframe.tensor.special.softplus	Compute the softplus function element-wise.

Convenience functions

maxframe.tensor.special.xlogy

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