theoretica::special Namespace Reference

Special functions. More...

Functions
real	gamma (unsigned int k)
	Gamma special function of positive integer argument. More...
real	half_gamma (unsigned int k)
	Half Gamma special function, defined as HG(n) = Gamma(n / 2) for any positive integer n. More...
real	lngamma (real x)
	Log Gamma special function of real argument. More...
real	gamma (real x)
	Gamma special function of real argument. More...
real	pi (real x)
	Pi special function of real argument. More...
real	beta (real x1, real x2)
	Beta special function of real argument. More...

Detailed Description

Special functions.

Function Documentation

beta()

real theoretica::special::beta ( real  x1, real  x2  )

inline

Beta special function of real argument.

Parameters

x1	The first real argument
x2	The second real argument

Returns

The Beta function of x1 and x2

gamma() [1/2]

real theoretica::special::gamma ( real  x )

inline

Gamma special function of real argument.

This function uses Lanczos' approximation with gamma = 5.

Parameters

x	The real argument

Returns

The Gamma function of x

gamma() [2/2]

real theoretica::special::gamma ( unsigned int  k )

inline

Gamma special function of positive integer argument.

Parameters

k	The positive integer argument

Returns

The Gamma function computed using the factorial.

half_gamma()

real theoretica::special::half_gamma ( unsigned int  k )

inline

Half Gamma special function, defined as HG(n) = Gamma(n / 2) for any positive integer n.

Parameters

k	The positive integer argument

Returns

The Gamma function computed using the factorial or double factorial identity.

lngamma()

real theoretica::special::lngamma ( real  x )

inline

Log Gamma special function of real argument.

This function uses Lanczos' approximation with gamma = 5.

Parameters

x	The real argument

Returns

The logarithm of the Gamma function of x

pi()

real theoretica::special::pi ( real  x )

inline

Pi special function of real argument.

Parameters

x	The real argument

Returns

The Pi function of x, equal to Gamma(x + 1)