Click or drag to resize

GammaRelated Class

Contains the gamma function and functions related to this function.
Inheritance Hierarchy
SystemObject
  Altaxo.CalcGammaRelated

Namespace: Altaxo.Calc
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
Syntax
C#
Copy
public class GammaRelated

The GammaRelated type exposes the following members.

Constructors
 NameDescription
Public methodGammaRelatedInitializes a new instance of the GammaRelated class
Top
Methods
 NameDescription
Public methodStatic memberBeta(Double, Double) Beta(a,b) calculates the complete beta function for double precision arguments a and b using Exp(LnBeta(a,b)).
Public methodStatic memberBeta(Double, Double, Boolean) Beta(a,b) calculates the complete beta function for double precision arguments a and b using Exp(LnBeta(a,b)).
Public methodStatic memberBetaI(Double, Double, Double) BetaI(x,a,b) calculates the double precision incomplete beta function. BetaI(x,a,b) = Integral(0,x) t**(a-1) (1-t)**(b-1) dt
Public methodStatic memberBetaI(Double, Double, Double, Boolean) BetaI(x,a,b) calculates the double precision incomplete beta function. BetaI(x,a,b) = Integral(0,x) t**(a-1) (1-t)**(b-1) dt
Public methodStatic memberBetaIR(Double, Double, Double) BetaIR(x,a,b) calculates the double precision incomplete beta function ratio.
C#
Copy
            B_x(a,b)    Integral(0,x) t**(a-1) (1-t)**(b-1) dt
I_x(a,b) = --------- = ---------------------------------------
            B(a,b)                   B(a,b)
Public methodStatic memberBetaIR(Double, Double, Double, Boolean) BetaIR(x,a,b) calculates the double precision incomplete beta function ratio.
C#
Copy
            B_x(a,b)    Integral(0,x) t**(a-1) (1-t)**(b-1) dt
I_x(a,b) = --------- = ---------------------------------------
            B(a,b)                   B(a,b)
Public methodStatic memberBetaRegularized BetaRegularized(x,a,b) calculates the double precision incomplete beta function ratio.
C#
Copy
            B_x(a,b)    Integral(0,x) t**(a-1) (1-t)**(b-1) dt
I_x(a,b) = --------- = ---------------------------------------
            B(a,b)                   B(a,b)
Public methodStatic memberBinomial Gives the binomial coefficient ( n over m).
Public methodEqualsDetermines whether the specified object is equal to the current object.
(Inherited from Object)
Public methodStatic memberFac(Int32) Fac(n) calculates the double precision factorial for the integer argument n.
Public methodStatic memberFac(Int32, Boolean) Fac(n) calculates the double precision factorial for the integer argument n.
Protected methodFinalizeAllows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object)
Public methodStatic memberGamma(Complex) Complex64T Gamma function.
Public methodStatic memberGamma(Double) Gamma(x) calculates the double precision complete Gamma function for double precision argument x.
Public methodStatic memberGamma(Complex, Boolean) Complex64T Gamma function.
Public methodStatic memberGamma(Double, Boolean) Gamma(x) calculates the double precision complete Gamma function for double precision argument x.
Public methodStatic memberGamma(Double, Double) Evaluate the complementary incomplete Gamma function Gamma(a,z0) = integral from z0 to infinity of exp(-t) * t**(a-1) The order of parameters is the same as the Mathematica function Gamma[a,z0]. Gamma(a,z0) is evaluated for arbitrary real values of A and for non-negative values of x (even though Gamma is defined for z0 < 0.0), except that for z0 = 0 and a <= 0.0, Gamma is undefined.
Public methodStatic memberGamma(Double, Double, Boolean) Evaluate the complementary incomplete Gamma function Gamma(a,z0) = integral from z0 to infinity of exp(-t) * t**(a-1) The order of parameters is the same as the Mathematica function Gamma[a,z0]. Gamma(a,z0) is evaluated for arbitrary real values of A and for non-negative values of x (even though Gamma is defined for z0 < 0.0), except that for z0 = 0 and a <= 0.0, Gamma is undefined.
Public methodStatic memberGammaI Evaluate the incomplete gamma function defined by GammaI = integral from t = 0 to x of exp(-t) * t**(a-1.0) GammaI(x,a) is evaluated for positive values of a and non-negative values of x. A slight deterioration of 2 or 3 digits accuracy will occur when GammaI is very large or very small, because logarithmic variables are used. The function and both arguments are double precision.
Public methodStatic memberGammaIC(Double, Double) Evaluate the complementary incomplete Gamma function GammaIC(x,a) = integral from x to infinity of exp(-t) * t**(a-1) GammaIC(x,a) is evaluated for arbitrary real values of A and for non-negative values of x (even though GammaIC is defined for x < 0.0), except that for x = 0 and a <= 0.0, GammaIC is undefined.
Public methodStatic memberGammaIC(Double, Double, Boolean) Evaluate the complementary incomplete Gamma function GammaIC(x,a) = integral from x to infinity of exp(-t) * t**(a-1) GammaIC(x,a) is evaluated for arbitrary real values of A and for non-negative values of x (even though GammaIC is defined for x < 0.0), except that for x = 0 and a <= 0.0, GammaIC is undefined.
Public methodStatic memberGammaIT(Double, Double) GammaIT(x,a) evaluates Tricomi's incomplete gamma function defined by GammaIT = x**(-a)/Gamma(a) * integral from 0 to x of exp(-t) * t**(a-1.0) for a > 0.0 and by analytic continuation for a <= 0.0. Gamma(x) is the complete gamma function of x.
Public methodStatic memberGammaIT(Double, Double, Boolean) GammaIT(x,a) evaluates Tricomi's incomplete gamma function defined by GammaIT = x**(-a)/Gamma(a) * integral from 0 to x of exp(-t) * t**(a-1.0) for a > 0.0 and by analytic continuation for a <= 0.0. Gamma(x) is the complete gamma function of x.
Public methodStatic memberGammaRegularized(Double, Double) Evaluate the incomplete regularized Gamma function GammaRegularized(a,z) = { integral from z to infinity of exp(-t) * t**(a-1) } / Gamma(a) The order of parameters is the same as the Mathematica function GammaRegularized[a,z].
Public methodStatic memberGammaRegularized(Double, Double, Double) Evaluate the incomplete regularized Gamma function Gamma(a,z0,z1) = { integral from z0 to z1 of exp(-t) * t**(a-1) }/Gamma(a) The order of parameters is the same as the Mathematica function GammaRegularized[a,z0,z1].
Public methodGetHashCodeServes as the default hash function.
(Inherited from Object)
Public methodGetTypeGets the Type of the current instance.
(Inherited from Object)
Public methodStatic memberInverseBetaRegularized InverseBetaRegularized gives the inverse of the incomplete beta function ratio (BetaIR(Double, Double, Double) or BetaRegularized(Double, Double, Double)).
Public methodStatic memberInverseGammaRegularized 
Public methodStatic memberLnBeta(Double, Double) LnBeta(a,b) calculates the double precision natural logarithm of the complete beta function for double precision arguments a and b.
Public methodStatic memberLnBeta(Double, Double, Boolean) LnBeta(a,b) calculates the double precision natural logarithm of the complete beta function for double precision arguments a and b.
Public methodStatic memberLnGamma(Complex) Complex64T logarithm of the gamma function.
Public methodStatic memberLnGamma(Double) Calculates the double precision logarithm of the absolute value of the Gamma function for double precision argument x.
Public methodStatic memberLnGamma(Complex, Boolean) Complex64T logarithm of the gamma function.
Public methodStatic memberLnGamma(Double, Boolean) Calculates the double precision logarithm of the absolute value of the Gamma function for double precision argument x.
Public methodStatic memberLnGamma(Double, Double) LnGamma(x,sgn) returns the double precision natural logarithm of the absolute value of the Gamma function for double precision argument x. The sign of the gamma function is returned in sgn.
Public methodStatic memberLnGamma(Double, Double, Boolean) LnGamma(x,sgn) returns the double precision natural logarithm of the absolute value of the Gamma function for double precision argument x. The sign of the gamma function is returned in sgn.
Public methodStatic memberLogBinomial Gives the natural logarithm of the binomial coefficient ( n over m).
Protected methodMemberwiseCloneCreates a shallow copy of the current Object.
(Inherited from Object)
Public methodToStringReturns a string that represents the current object.
(Inherited from Object)
Top
See Also