﻿SpecialFunctions Class   # SpecialFunctions Class

This class contains a collection of special functions. Inheritance Hierarchy
SystemObject
CenterSpace.NMath.CoreSpecialFunctions

Namespace: CenterSpace.NMath.Core
Assembly: NMath (in NMath.dll) Version: 7.4 Syntax
`public class SpecialFunctions`

The SpecialFunctions type exposes the following members. Constructors
NameDescription SpecialFunctionsInitializes a new instance of the SpecialFunctions class
Top Methods
NameDescription  Airy The Airy and Bairy functions are the two solutions of the differential equation
C#
`y''(x) = xy`
.  BesselI0 Modified Bessel function of the first kind, order zero.  BesselI1 Modified Bessel function of the first kind, first order.  BesselIv Modified Bessel function of the first kind, non-integer order. Zero is returned if
C#
`x < 0`
and n is not an integer.  BesselJ0 Bessel function of the first kind, order zero.  BesselJ1 Bessel function of the first kind, first order.  BesselJn Bessel function of the first kind, arbitrary integer order.  BesselJv Bessel function of first kind, non-integer order. Zero is returned if
C#
`x < 0`
and n is not an integer.  BesselK0 Modified Bessel function of the second kind, order zero.  BesselK1 Modified Bessel function of the second kind, order one.  BesselKn Modified Bessel function of the second kind, arbitrary integer order.  BesselY0 Bessel function of the second kind, order zero.  BesselY1 Bessel function of the second kind, order one.  BesselYn Bessel function of the second kind of integer order.  BesselYv Bessel function of the second kind, non-integer order..  Beta The beta function, beta(a, b) = Gamma(a) * Gamma(b) / Gamma(a+b). If either a or b = 0, -1, -2, ... then Double.NaN is returned.  Binomial Binomial coefficient (n choose k); The number of ways of picking k unordered outcomes from n possibilities.  BinomialLn Natural log of the binomial coefficient (n choose k); the number of ways of picking k unordered outcomes from n possibilities.  Cn Computes jacobian elliptic function Cn() for real, pure imaginary, or complex arguments.  Digamma The digamma or psi function, defined as Gamma'(z)/Gamma(z). A Double.NaN is return for all non-positive integers x = { 0, -1, -2, ... }.  Ei Exponential integral.  EllipJ The real valued Jacobi elliptic functions cn(), sn(), and dn().  EllipticE(Double) The complete elliptic integral, E(m), of the second kind.  EllipticE(Double, Double) The incomplete elliptic integral of the second kind.  EllipticF The incomplete elliptic integral of the first kind.  EllipticK The complete elliptic integral, K(m), of the first kind.  Factorial Factorial. The number of ways that n objects can be permuted.  FactorialLn Natural log factorial of n,
C#
`ln( n! )`
.  Gamma The gamma function. Returns
C#
`Double.NaN`
for all x = { 0, -1, -2, ... }.  GammaLn THe natural log of the gamma function. A Double.NaN is return for all x = { 0, -1, -2, ... }. and for all other negative values the real part is returned.  GammaReciprocal The reciprocal of the gamma function. For arguments larger than +34.84425627277176174 the reciprocal of Double.MaxValue is returned.  HarmonicNumber(Double) The harmonic number, Hn, which is a truncation of the harmonic series.  HarmonicNumber(Int32) The harmonic number, Hn, is a truncated sum of the harmonic series.  Hypergeometric1F1 The confluent hypergeometric series of the first kind.  Hypergeometric2F1 The Gauss or generalized hypergeometric function.  IncompleteBeta The incomplete beta function, with x defined over the domain of [0, 1].  IncompleteGamma The incomplete gamma integral. Both arguments must be positive.  IncompleteGammaComplement The complemented incomplete gamma integral. Both arguments must be positive.  NoncentralTDistributionCDF The CDF at x of the noncentral t-distribution  PolyLogarithm The polylogarithm, Li_n(x). Li_n(x) reduces to the Riemann zeta function for x = 1.  Sn Computes jacobian elliptic function Sn() for real, pure imaginary, or complex arguments.  Zeta The Riemann zeta function.
Top Fields
NameDescription  EulerGamma The Euler-Mascheroni constant, approximately equal to 0.5772156649...
Top See Also

#### Reference

CenterSpace.NMath.Core Namespace