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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: 7.4
Syntax
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public class SpecialFunctions

The SpecialFunctions type exposes the following members.

Constructors
 NameDescription
Public methodSpecialFunctionsInitializes 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
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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
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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
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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,
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ln( n! )
.
Public methodStatic memberGamma The gamma function. Returns
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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