Parameters
double z
The first Beta parameter, a positive real number.
double w
The second Beta parameter, a positive real number.
Return
double
The Euler Beta function evaluated at z,w.
Type SpecialFunctions
Namespace MathNet.Numerics
double zThe first Beta parameter, a positive real number.
double wThe second Beta parameter, a positive real number.
doubleThe Euler Beta function evaluated at z,w.
double aThe first Beta parameter, a positive real number.
double bThe second Beta parameter, a positive real number.
double xThe upper limit of the integral.
doubleThe lower incomplete (unregularized) beta function.
double zThe first Beta parameter, a positive real number.
double wThe second Beta parameter, a positive real number.
doubleThe logarithm of the Euler Beta function evaluated at z,w.
double aThe first Beta parameter, a positive real number.
double bThe second Beta parameter, a positive real number.
double xThe upper limit of the integral.
doubleThe regularized lower incomplete beta function.
int nA nonnegative value n.
int kA nonnegative value h.
doubleThe binomial coefficient: n choose k.
int nA nonnegative value n.
int kA nonnegative value h.
doubleThe logarithmic binomial coefficient: ln(n choose k).
double xThe argument of the digamma function.
doubleThe value of the DiGamma function at x.
Computes the inverse Digamma function: this is the inverse of the logarithm of the gamma function. This function will only return solutions that are positive.
This implementation is based on the bisection method.
double pThe argument of the inverse digamma function.
doubleThe positive solution to the inverse DiGamma function at p.
double xThe value to evaluate.
doublethe error function evaluated at given value.
double xThe value to evaluate.
doublethe complementary error function evaluated at given value.
We have tested this implementation against the arbitrary precision mpmath library and found cases where we can only guarantee 9 significant figures correct.
double zvalue to evaluate.
doubleThe complementary inverse error function evaluated at given value.
double zvalue to evaluate.
doubleThe inverse error function evaluated at given value.
x -> exp(x)-1
double powerA number specifying a power.
doubleReturns exp(power)-1.
If you need to multiply or divide various such factorials, consider using the logarithmic version FactorialLn instead so you can add instead of multiply and subtract instead of divide, and then exponentiate the result using Exp. This will also circumvent the problem that factorials become very large even for small parameters.
doubleA value value! for value > 0
doubleA value value! for value > 0
This implementation of the computation of the gamma and logarithm of the gamma function follows the derivation in "An Analysis Of The Lanczos Gamma Approximation", Glendon Ralph Pugh, 2004. We use the implementation listed on p. 116 which should achieve an accuracy of 16 floating point digits. Although 16 digit accuracy should be sufficient for double values, improving accuracy is possible (see p. 126 in Pugh).
Our unit tests suggest that the accuracy of the Gamma function is correct up to 13 floating point digits.
double zThe argument of the gamma function.
doubleThe logarithm of the gamma function.
This implementation of the computation of the gamma and logarithm of the gamma function follows the derivation in "An Analysis Of The Lanczos Gamma Approximation", Glendon Ralph Pugh, 2004. We use the implementation listed on p. 116 which achieves an accuracy of 16 floating point digits. Although 16 digit accuracy should be sufficient for double values, improving accuracy is possible (see p. 126 in Pugh).
Our unit tests suggest that the accuracy of the Gamma function is correct up to 14 floating point digits.
double zThe argument of the gamma function.
doubleThe logarithm of the gamma function.
double aThe argument for the gamma function.
double xThe upper integral limit.
doubleThe lower incomplete gamma function.
double aThe argument for the gamma function.
double xThe upper integral limit.
doubleThe lower incomplete gamma function.
double aThe argument for the gamma function.
double xThe lower integral limit.
doubleThe upper incomplete gamma function.
double aThe argument for the gamma function.
double xThe lower integral limit.
doubleThe upper incomplete regularized gamma function.
int nThe order parameter.
double mThe power parameter.
doubleGeneral Harmonic number.
int tThe Harmonic number which needs to be computed.
doubleThe t'th Harmonic number.
(a,b) -> sqrt(a^2 + b^2)
double aThe length of side a of the triangle.
double bThe length of side b of the triangle.
doubleReturns sqrt(a2 + b2) without underflow/overflow.
(a,b) -> sqrt(a^2 + b^2)
Complex aThe length of side a of the triangle.
Complex bThe length of side b of the triangle.
ComplexReturns sqrt(a2 + b2) without underflow/overflow.
(a,b) -> sqrt(a^2 + b^2)
float aThe length of side a of the triangle.
float bThe length of side b of the triangle.
floatReturns sqrt(a2 + b2) without underflow/overflow.
double pThe parameter for which to compute the logistic function.
doubleThe logistic function of p.
double pThe parameter for which to compute the logit function. This number should be between 0 and 1.
doubleThe logarithm of p divided by 1.0 - p.
int nA nonnegative value n.
Int32[] niAn array of nonnegative values that sum to n.
doubleThe multinomial coefficient.