- beta
real beta(real x, real y)
- betaIncomplete
real betaIncomplete(real a, real b, real x)
- betaIncompleteInverse
real betaIncompleteInverse(real a, real b, real y)
Inverse of incomplete beta integral
- digamma
real digamma(real x)
- erf
real erf(real x)
- 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)
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.