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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: 7.3
Syntax
public class SpecialFunctions

The SpecialFunctions type exposes the following members.

Constructors
  NameDescription
Public methodSpecialFunctions
Initializes a new instance of the SpecialFunctions class
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Methods
  NameDescription
Public methodStatic memberAiry
The Airy and Bairy functions are the two solutions of the differential equation
y''(x) = xy
.
Public methodStatic memberBesselI0
Modified Bessel function of the first kind, order zero.
Public methodStatic memberBesselI1
Modified Bessel function of the first kind, first order.
Public methodStatic memberBesselIv
Modified Bessel function of the first kind, non-integer order. Zero is returned if
x < 0
and n is not an integer.
Public methodStatic memberBesselJ0
Bessel function of the first kind, order zero.
Public methodStatic memberBesselJ1
Bessel function of the first kind, first order.
Public methodStatic memberBesselJn
Bessel function of the first kind, arbitrary integer order.
Public methodStatic memberBesselJv
Bessel function of first kind, non-integer order. Zero is returned if
x < 0
and n is not an integer.
Public methodStatic memberBesselK0
Modified Bessel function of the second kind, order zero.
Public methodStatic memberBesselK1
Modified Bessel function of the second kind, order one.
Public methodStatic memberBesselKn
Modified Bessel function of the second kind, arbitrary integer order.
Public methodStatic memberBesselY0
Bessel function of the second kind, order zero.
Public methodStatic memberBesselY1
Bessel function of the second kind, order one.
Public methodStatic memberBesselYn
Bessel function of the second kind of integer order.
Public methodStatic memberBesselYv
Bessel function of the second kind, non-integer order..
Public methodStatic memberBeta
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.
Public methodStatic memberBinomial
Binomial coefficient (n choose k); The number of ways of picking k unordered outcomes from n possibilities.
Public methodStatic memberBinomialLn
Natural log of the binomial coefficient (n choose k); the number of ways of picking k unordered outcomes from n possibilities.
Public methodStatic memberCn
Computes jacobian elliptic function Cn() for real, pure imaginary, or complex arguments.
Public methodStatic memberDigamma
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, ... }.
Public methodStatic memberEi
Exponential integral.
Public methodStatic memberEllipJ
The real valued Jacobi elliptic functions cn(), sn(), and dn().
Public methodStatic memberEllipticE(Double)
The complete elliptic integral, E(m), of the second kind.
Public methodStatic memberEllipticE(Double, Double)
The incomplete elliptic integral of the second kind.
Public methodStatic memberEllipticF
The incomplete elliptic integral of the first kind.
Public methodStatic memberEllipticK
The complete elliptic integral, K(m), of the first kind.
Public methodStatic memberFactorial
Factorial. The number of ways that n objects can be permuted.
Public methodStatic memberFactorialLn
Natural log factorial of n,
ln( n! )
.
Public methodStatic memberGamma
The gamma function. Returns
Double.NaN
for all x = { 0, -1, -2, ... }.
Public methodStatic memberGammaLn
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.
Public methodStatic memberGammaReciprocal
The reciprocal of the gamma function. For arguments larger than +34.84425627277176174 the reciprocal of Double.MaxValue is returned.
Public methodStatic memberHarmonicNumber(Double)
The harmonic number, Hn, which is a truncation of the harmonic series.
Public methodStatic memberHarmonicNumber(Int32)
The harmonic number, Hn, is a truncated sum of the harmonic series.
Public methodStatic memberHypergeometric1F1
The confluent hypergeometric series of the first kind.
Public methodStatic memberHypergeometric2F1
The Gauss or generalized hypergeometric function.
Public methodStatic memberIncompleteBeta
The incomplete beta function, with x defined over the domain of [0, 1].
Public methodStatic memberIncompleteGamma
The incomplete gamma integral. Both arguments must be positive.
Public methodStatic memberIncompleteGammaComplement
The complemented incomplete gamma integral. Both arguments must be positive.
Public methodStatic memberNoncentralTDistributionCDF
The CDF at x of the noncentral t-distribution
Public methodStatic memberPolyLogarithm
The polylogarithm, Li_n(x). Li_n(x) reduces to the Riemann zeta function for x = 1.
Public methodStatic memberSn
Computes jacobian elliptic function Sn() for real, pure imaginary, or complex arguments.
Public methodStatic memberZeta
The Riemann zeta function.
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Fields
  NameDescription
Public fieldStatic memberEulerGamma
The Euler-Mascheroni constant, approximately equal to 0.5772156649...
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See Also