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Gamma Struct Reference

Evaluate the Gamma function and several related functions. More...

#include <Gamma.h>

List of all members.

Static Public Member Functions

double lnGammaAbs (const double x)
 Evaluate ln[Gamma(x)], x not a negative integer. Returns ln[|Gamma(x)|] when x < 0.

Dpair lnGammaAbsErr (const double x)
 Evaluate ln[Gamma(x)], x not a negative integer and estimate the error.

Dpair lnGamma (const double x)
 Evaluate ln[Gamma(x)], x not a negative integer. Returns ln[|Gamma(x)|] when x < 0.

Dpair lnGammaErr (const double x)
 Evaluate ln[Gamma(x)], x not a negative integer and estimate the error.

double GammaFunction (const double x)
 Evaluate Gamma(x), x not a negative integer.

Dpair GammaFunctionErr (const double x)
 Evaluate Gamma(x), x not a negative integer, and estimate the error.

double GammaStar (const double x)
 Evaluate the Regulated Gamma(x) function, x > 0.

Dpair GammaStarErr (const double x)
 Evaluate the Regulated Gamma(x) function, x > 0 and estimate the error.

double ReciprocalGamma (const double x)
 Evaluate the reciprocal Gamma functions.

Dpair ReciprocalGammaErr (const double x)
 Evaluate the reciprocal Gamma functions and estimate the error.

Dpair lnGammaZ (const Dcomplex x)
 Evaluate ln[Gamma(z)] for complex z, z not a negative integer.

Dpair lnGammaZErr (const Dcomplex x)
 Evaluate ln[Gamma(z)] for complex z, z not a negative integer, and estimate the error.

double TaylorN (const int n, const double x)
 Evaluate the Taylor coefficent x^n/n!

Dpair TaylorNErr (const int n, const double x)
 Evaluate the Taylor coefficent x^n/n! and estimate the error.

double Factorial (const unsigned int n)
 Evaluate n!

Dpair FactorialErr (const unsigned int n)
 Evaluate n! and estimate the error.

double DoubleFactorial (const unsigned int n)
 Evaluate n!!

Dpair DoubleFactorialErr (const unsigned int n)
 Evaluate n!! and estimate the error.

double lnFactorial (const unsigned int n)
 Evaluate ln(n!) (Alleged to be faster than ln[Gamma(n+1)]).

Dpair lnFactorialErr (const unsigned int n)
 Evaluate ln(n!) (Alleged to be faster than ln[Gamma(n+1)]) and estimate the error.

double lnDoubleFactorial (const unsigned int n)
 Evaluate ln(n!!).

Dpair lnDoubleFactorialErr (const unsigned int n)
 Evaluate ln(n!!) and estimate the error.

double lnBinomialCoefficient (const unsigned int n, const unsigned int m)
 Evaluate ln(n choose m) e. g., ln[Binomial Coefficient(n,m)].

Dpair lnBinomialCoefficientErr (const unsigned int n, const unsigned int m)
 Evaluate ln(n choose m) and estimate the error.

double BinomialCoefficient (const unsigned int n, const unsigned int m)
 Evaluate (n choose m).

Dpair BinomialCoefficientErr (const unsigned int n, const unsigned int m)
 Evaluate (n choose m) and estimate the error.

double lnPochammer (const double a, const double x)
 Evaluate ln(|a_x|) where a_x is the Pochammer symbol, Gamma(a+x)/Gamma(a).

Dpair lnPochammerErr (const double a, const double x)
 Evaluate ln(|a_x|) where a_x is the Pochammer symbol, Gamma(a+x)/Gamma(a) and estimate the error.

Dpair lnPochammerSign (const double a, const double x)
 Evaluate ln(a_x) where a_x is the Pochammer symbol, Gamma(a+x)/Gamma(a) with the correct sign attached.

Dpair lnPochammerSignErr (const double a, const double x)
 Evaluate ln(a_x) where a_x is the Pochammer symbol, Gamma(a+x)/Gamma(a) with the correct sign attached and estimate the error.

double Pochammer (const double a, const double x)
 Evaluate a_x where a_x is the Pochammer symbol, Gamma(a+x)/Gamma(a).

Dpair PochammerErr (const double a, const double x)
 Evaluate a_x where a_x is the Pochammer symbol, Gamma(a+x)/Gamma(a) and estimate the error.

double RelativePochammer (const double a, const double x)
 Evaluate the relative Pochammer symbol, (a_x -1)/x.

Dpair RelativePochammerErr (const double a, const double x)
 Evaluate the relative Pochammer symbol, (a_x -1)/x and estimate the error.

double IncompleteGamma (const double a, const double x)
 Evaluate the Normalized Incomplete Gamma function.

Dpair IncompleteGammaErr (const double a, const double x)
 Evaluate the Normalized Incomplete Gamma function and estimate the error.

double CompIncompleteGamma (const double a, const double x)
 Evaluate the Complementary Normalized Incomplete Gamma function.

Dpair CompIncompleteGammaErr (const double a, const double x)
 Evaluate the Complementary Normalized Incomplete Gamma function and estimate the error.

double lnBeta (const double a, const double b)
 Evaluate the logarithm of the Beta function.

Dpair lnBetaErr (const double a, const double b)
 Evaluate the logarithm of the Beta function and estimate the error.

double Beta (const double a, const double b)
 Evaluate the Beta function.

Dpair BetaErr (const double a, const double b)
 Evaluate the Beta function and estimate the error.

double IncompleteBeta (const double a, const double b, const double x)
 Evaluate the Normalized Incomplete Beta function.

Dpair IncompleteBetaErr (const double a, const double b, const double x)
 Evaluate the Normalized Incomplete Beta function and estimate the error.

Detailed Description

Evaluate the Gamma function and several related functions.

Definition at line 27 of file Gamma.h.

Member Function Documentation

double Gamma::Beta (  const double  a,
const double  b
)  [static]
 

Evaluate the Beta function.

Dpair Gamma::BetaErr (  const double  a,
const double  b
)  [static]
 

Evaluate the Beta function and estimate the error.

double Gamma::BinomialCoefficient (  const unsigned int  n,
const unsigned int  m
)  [static]
 

Evaluate (n choose m).

Dpair Gamma::BinomialCoefficientErr (  const unsigned int  n,
const unsigned int  m
)  [static]
 

Evaluate (n choose m) and estimate the error.

double Gamma::CompIncompleteGamma (  const double  a,
const double  x
)  [static]
 

Evaluate the Complementary Normalized Incomplete Gamma function.

Dpair Gamma::CompIncompleteGammaErr (  const double  a,
const double  x
)  [static]
 

Evaluate the Complementary Normalized Incomplete Gamma function and estimate the error.

double Gamma::DoubleFactorial (  const unsigned int  n  )  [static]
 

Evaluate n!!

Dpair Gamma::DoubleFactorialErr (  const unsigned int  n  )  [static]
 

Evaluate n!! and estimate the error.

double Gamma::Factorial (  const unsigned int  n  )  [static]
 

Evaluate n!

Dpair Gamma::FactorialErr (  const unsigned int  n  )  [static]
 

Evaluate n! and estimate the error.

double Gamma::GammaFunction (  const double  x  )  [static]
 

Evaluate Gamma(x), x not a negative integer.

Dpair Gamma::GammaFunctionErr (  const double  x  )  [static]
 

Evaluate Gamma(x), x not a negative integer, and estimate the error.

double Gamma::GammaStar (  const double  x  )  [static]
 

Evaluate the Regulated Gamma(x) function, x > 0.

Dpair Gamma::GammaStarErr (  const double  x  )  [static]
 

Evaluate the Regulated Gamma(x) function, x > 0 and estimate the error.

double Gamma::IncompleteBeta (  const double  a,
const double  b,
const double  x
)  [static]
 

Evaluate the Normalized Incomplete Beta function.

Dpair Gamma::IncompleteBetaErr (  const double  a,
const double  b,
const double  x
)  [static]
 

Evaluate the Normalized Incomplete Beta function and estimate the error.

double Gamma::IncompleteGamma (  const double  a,
const double  x
)  [static]
 

Evaluate the Normalized Incomplete Gamma function.

Dpair Gamma::IncompleteGammaErr (  const double  a,
const double  x
)  [static]
 

Evaluate the Normalized Incomplete Gamma function and estimate the error.

double Gamma::lnBeta (  const double  a,
const double  b
)  [static]
 

Evaluate the logarithm of the Beta function.

Dpair Gamma::lnBetaErr (  const double  a,
const double  b
)  [static]
 

Evaluate the logarithm of the Beta function and estimate the error.

double Gamma::lnBinomialCoefficient (  const unsigned int  n,
const unsigned int  m
)  [static]
 

Evaluate ln(n choose m) e. g., ln[Binomial Coefficient(n,m)].

Dpair Gamma::lnBinomialCoefficientErr (  const unsigned int  n,
const unsigned int  m
)  [static]
 

Evaluate ln(n choose m) and estimate the error.

double Gamma::lnDoubleFactorial (  const unsigned int  n  )  [static]
 

Evaluate ln(n!!).

Dpair Gamma::lnDoubleFactorialErr (  const unsigned int  n  )  [static]
 

Evaluate ln(n!!) and estimate the error.

double Gamma::lnFactorial (  const unsigned int  n  )  [static]
 

Evaluate ln(n!) (Alleged to be faster than ln[Gamma(n+1)]).

Dpair Gamma::lnFactorialErr (  const unsigned int  n  )  [static]
 

Evaluate ln(n!) (Alleged to be faster than ln[Gamma(n+1)]) and estimate the error.

Dpair Gamma::lnGamma (  const double  x  )  [static]
 

Evaluate ln[Gamma(x)], x not a negative integer. Returns ln[|Gamma(x)|] when x < 0.

double Gamma::lnGammaAbs (  const double  x  )  [static]
 

Evaluate ln[Gamma(x)], x not a negative integer. Returns ln[|Gamma(x)|] when x < 0.

Dpair Gamma::lnGammaAbsErr (  const double  x  )  [static]
 

Evaluate ln[Gamma(x)], x not a negative integer and estimate the error.

Evaluate ln[Gamma(x)], x not a negative integer and estimate the error Returns ln[Gamma(x)] with proper sign when x < 0

Dpair Gamma::lnGammaErr (  const double  x  )  [static]
 

Evaluate ln[Gamma(x)], x not a negative integer and estimate the error.

Evaluate ln[Gamma(x)], x not a negative integer and estimate the error. Returns ln[Gamma(x)] with proper sign when x < 0

Dpair Gamma::lnGammaZ (  const Dcomplex  x  )  [static]
 

Evaluate ln[Gamma(z)] for complex z, z not a negative integer.

Dpair Gamma::lnGammaZErr (  const Dcomplex  x  )  [static]
 

Evaluate ln[Gamma(z)] for complex z, z not a negative integer, and estimate the error.

double Gamma::lnPochammer (  const double  a,
const double  x
)  [static]
 

Evaluate ln(|a_x|) where a_x is the Pochammer symbol, Gamma(a+x)/Gamma(a).

Dpair Gamma::lnPochammerErr (  const double  a,
const double  x
)  [static]
 

Evaluate ln(|a_x|) where a_x is the Pochammer symbol, Gamma(a+x)/Gamma(a) and estimate the error.

Dpair Gamma::lnPochammerSign (  const double  a,
const double  x
)  [static]
 

Evaluate ln(a_x) where a_x is the Pochammer symbol, Gamma(a+x)/Gamma(a) with the correct sign attached.

Dpair Gamma::lnPochammerSignErr (  const double  a,
const double  x
)  [static]
 

Evaluate ln(a_x) where a_x is the Pochammer symbol, Gamma(a+x)/Gamma(a) with the correct sign attached and estimate the error.

double Gamma::Pochammer (  const double  a,
const double  x
)  [static]
 

Evaluate a_x where a_x is the Pochammer symbol, Gamma(a+x)/Gamma(a).

Dpair Gamma::PochammerErr (  const double  a,
const double  x
)  [static]
 

Evaluate a_x where a_x is the Pochammer symbol, Gamma(a+x)/Gamma(a) and estimate the error.

double Gamma::ReciprocalGamma (  const double  x  )  [static]
 

Evaluate the reciprocal Gamma functions.

Dpair Gamma::ReciprocalGammaErr (  const double  x  )  [static]
 

Evaluate the reciprocal Gamma functions and estimate the error.

double Gamma::RelativePochammer (  const double  a,
const double  x
)  [static]
 

Evaluate the relative Pochammer symbol, (a_x -1)/x.

Dpair Gamma::RelativePochammerErr (  const double  a,
const double  x
)  [static]
 

Evaluate the relative Pochammer symbol, (a_x -1)/x and estimate the error.

double Gamma::TaylorN (  const int  n,
const double  x
)  [static]
 

Evaluate the Taylor coefficent x^n/n!

Dpair Gamma::TaylorNErr (  const int  n,
const double  x
)  [static]
 

Evaluate the Taylor coefficent x^n/n! and estimate the error.

The documentation for this struct was generated from the following file:
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