﻿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
SpecialFunctions
Initializes a new instance of the SpecialFunctions class
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Methods
NameDescription
Airy
The Airy and Bairy functions are the two solutions of the differential equation
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
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
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,
ln( n! )
.
Gamma
The gamma function. Returns
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.
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Fields
NameDescription
EulerGamma
The Euler-Mascheroni constant, approximately equal to 0.5772156649...
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