std.mathspecial

Mathematical Special Functions

The technical term 'Special Functions' includes several families of transcendental functions, which have important applications in particular branches of mathematics and physics.

The gamma and related functions, and the error function are crucial for mathematical statistics. The Bessel and related functions arise in problems involving wave propagation (especially in optics). Other major categories of special functions include the elliptic integrals (related to the arc length of an ellipse), and the hypergeometric functions.

Status: Many more functions will be added to this module. The naming convention for the distribution functions (gammaIncomplete, etc) is not yet finalized and will probably change.

fn beta betaIncomplete betaIncompleteInverse digamma erf erfc gamma gammaIncomplete gammaIncompleteCompl gammaIncompleteComplInverse logGamma logmdigamma logmdigammaInverse normalDistribution normalDistributionInverse sgnGamma

Functions 16

fnreal gamma(real x)The Gamma function, (x)

fnreal logGamma(real x)Natural logarithm of the gamma function, (x)

fnreal sgnGamma(real x)The sign of (x).

fnreal beta(real x, real y)Beta function, B(x,y)

fnreal digamma(real x)Digamma function, (x)

fnreal logmdigamma(real x)Log Minus Digamma function

fnreal logmdigammaInverse(real x)Inverse of the Log Minus Digamma function

fnreal betaIncomplete(real a, real b, real x )Incomplete beta integral

fnreal betaIncompleteInverse(real a, real b, real y )Inverse of incomplete beta integral

fnreal gammaIncomplete(real a, real x )Incomplete gamma integral and its complement

fnreal gammaIncompleteCompl(real a, real x )ditto

fnreal gammaIncompleteComplInverse(real a, real p)Inverse of complemented incomplete gamma integral

fnreal erf(real x)Error function

fnreal erfc(real x)Complementary error function

fnreal normalDistribution(real x)Standard normal distribution function.

fnreal normalDistributionInverse(real p)Inverse of Standard normal distribution function