# 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.

## Public Imports

std.math
public import std.math;
Undocumented in source.

## Members

### Functions

beta
real beta(real x, real y)

Beta function

betaIncomplete
real betaIncomplete(real a, real b, real x)

Incomplete beta integral

betaIncompleteInverse
real betaIncompleteInverse(real a, real b, real y)

Inverse of incomplete beta integral

digamma
real digamma(real x)

Digamma function

erf
real erf(real x)

Error function

erfc
real erfc(real x)

Complementary error function

gamma
real gamma(real x)

The Gamma function, \$(GAMMA)(x)

gammaIncomplete
real gammaIncomplete(real a, real x)
gammaIncompleteCompl
real gammaIncompleteCompl(real a, real x)

Incomplete gamma integral and its complement

gammaIncompleteComplInverse
real gammaIncompleteComplInverse(real a, real p)

Inverse of complemented incomplete gamma integral

logGamma
real logGamma(real x)

Natural logarithm of the gamma function, \$(GAMMA)(x)

logmdigamma
real logmdigamma(real x)

Log Minus Digamma function

logmdigammaInverse
real logmdigammaInverse(real x)

Inverse of the Log Minus Digamma function

normalDistribution
real normalDistribution(real x)

Standard normal distribution function.

normalDistributionInverse
real normalDistributionInverse(real p)

Inverse of Standard normal distribution function

sgnGamma
real sgnGamma(real x)

The sign of \$(GAMMA)(x).