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Gamma Class |
Inheritance HierarchyAccord.MathGamma
Namespace: Accord.Math
Assembly: Accord.Math (in Accord.Math.dll) Version: 3.8.0
SyntaxThe Gamma type exposes the following members.
Methods| Name | Description | |
|---|---|---|
  | Digamma |
Digamma function.
|
| Function |
Gamma function of the specified value.
|
| Inverse |
Inverse of the complemented
incomplete Gamma integral (UpperIncomplete, Q).
|
| InverseLowerIncomplete |
Inverse of the
incomplete Gamma integral (LowerIncomplete, P).
|
| InverseUpperIncomplete |
Inverse of the complemented
incomplete Gamma integral (UpperIncomplete, Q).
|
| Log(Double) |
Natural logarithm of the gamma function.
|
| Log(Double, Int32) |
Natural logarithm of the multivariate Gamma function.
|
| LowerIncomplete |
Lower incomplete regularized gamma function P
(a.k.a. the incomplete Gamma function).
|
| Multivariate |
Multivariate Gamma function
|
| Stirling |
Gamma function as computed by Stirling's formula.
|
| Trigamma |
Trigamma function.
|
| UpperIncomplete |
Upper incomplete regularized Gamma function Q
(a.k.a the incomplete complemented Gamma function)
|
Fields
RemarksIn mathematics, the gamma function (represented by the capital Greek letter Γ) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers. That is, if n is a positive integer:
Γ(n) = (n-1)!The gamma function is defined for all complex numbers except the negative integers and zero. For complex numbers with a positive real part, it is defined via an improper integral that converges:
∞ Γ(z) = ∫ t^(z-1)e^(-t) dt 0
This integral function is extended by analytic continuation to all complex numbers except the non-positive integers (where the function has simple poles), yielding the meromorphic function we call the gamma function.
The gamma function is a component in various probability-distribution functions, and as such it is applicable in the fields of probability and statistics, as well as combinatorics.
References:
- Wikipedia contributors, "Gamma function,". Wikipedia, The Free Encyclopedia. Available at: http://en.wikipedia.org/wiki/Gamma_function
- Cephes Math Library, http://www.netlib.org/cephes/
Examplesdouble x = 0.17; // Compute main Gamma function and variants double gamma = Gamma.Function(x); // 5.4511741801042106 double gammap = Gamma.Function(x, p: 2); // -39.473585841300675 double log = Gamma.Log(x); // 1.6958310313607003 double logp = Gamma.Log(x, p: 2); // 3.6756317353404273 double stir = Gamma.Stirling(x); // 24.040352622960743 double psi = Gamma.Digamma(x); // -6.2100942259248626 double tri = Gamma.Trigamma(x); // 35.915302055854525 double a = 4.2; // Compute the incomplete regularized Gamma functions P and Q: double lower = Gamma.LowerIncomplete(a, x); // 0.000015685073063633753 double upper = Gamma.UpperIncomplete(a, x); // 0.9999843149269364
See Also