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ExtMathC::Factorial(UIntT) ExtMathC::RFactorial(UIntT) ExtMathC::LnFactorial(UIntT) ExtMathC::RBinomCoeff(IntT,IntT) ExtMathC::Beta(RealT,RealT) ExtMathC::Betai(RealT,RealT,RealT) ExtMathC::BesselIo(const RealT) ExtMathC::LnGamma(RealT) ExtMathC::GammaP(RealT,RealT) ExtMathC::GammaQ(RealT,RealT) ExtMathC::Chi2P(IntT,RealT) ExtMathC::Chi2Q(IntT,RealT) ExtMathC::CumPoissonP(IntT,RealT) ExtMathC::Init(void) ExtMathC::GammaPSeries(RealT,RealT) ExtMathC::GammaQContFrac(RealT,RealT) ExtMathC::BetaCF(RealT,RealT,RealT)

ExtMathC
The class ExtMathC is a collection of special higher transcendental functions.
include	"amma/ScalMath.hh"
User Level:	Default
Library:	Mmath
Example:	exComplx.cc
Section:	Basic Types.Numerical
In Scope:	std

Derived Classes:

SDFunction1dC

IntT init;

The variable of initialization;

RealT incGammaRelPrecision;

The relative precision of evaluation of the incomplete gamma function.

const IntT factorialSize = 32;

The number of precomputed factorials.

RealT factorial[];

The table of precomputed factorials.

const IntT factorialSize;

The number of precomputed factorials.

IntT Factorial(UIntT n)

Returns the factorial of the integer 'n'. The result is computed using integer arithmetic.

RealT RFactorial(UIntT n)

Returns the factorial of the integer 'n'. The result is computed using real arithmetic. The returned values for 'n' < factorialSize are pre-computed.

RealT LnFactorial(UIntT n)

Returns ln(n!).

RealT RBinomCoeff(IntT n,IntT k)

Returns the binomial coefficient (n over k) as a real number.

RealT Beta(RealT z,RealT w)

Returns the value the beta function B(z,w).

RealT Betai(RealT a,RealT b,RealT x)

Returns the value the incomplete beta function Ix(a,b)

RealT BesselIo(const RealT x)

Returns the value of the modified Bessel function of the first kind and zero order. Gamma function and its modifications ------------------------------------

RealT LnGamma(RealT x)

Returns the value ln(Gamma(x)) for x > 0.

RealT GammaP(RealT a,RealT x)

Returns the value of the incomplete gama function P(a,x) for a >0 and x >= 0.

RealT GammaQ(RealT a,RealT x)

Returns the value of the complement Q(a,x)=1-P(x,a) of the incomplete gama function P(a,x) for a >0 and x >= 0.

RealT Chi2P(IntT f,RealT chi2)

Returns the value of the chi-square probability function that is the probability that the observed chi-square for a correct model should be less than a value 'chi2'. The parameter 'f' is the number of degrees of freedom.

RealT Chi2Q(IntT f,RealT chi2)

Returns the value of the complement of the chi-square probability function that is the probability that the observed chi-square will exceed the value 'chi2' by chance even for a correct model. The parameter 'f' is the number of degrees of freedom.

RealT CumPoissonP(IntT k,RealT m)

Returns the value of the cumulative Poisson probability function that is defined as the probability that the number of Poisson random events occuring will be between 0 and (k-1) inclusive, if the expected mean number is 'm'.

IntT Init()

Initialization of the class. Gamma function - evaluation methods -----------------------------------

RealT GammaPSeries(RealT a,RealT x)

Returns the value of the incomplete gama function P(a,x) for a >0 and x >= 0 evaluated by its series representation.

RealT GammaQContFrac(RealT a,RealT x)

Returns the value of the incomplete gama function Q(a,x) for a >0 and x >= 0 evaluated by its contiued fraction representation. The test of convergence is not sufficient for x < (a+1).

RealT BetaCF(RealT a,RealT b,RealT x)

Used by BetaI to evaluate the continued fraction for incomplete beta function by modified Lentz's method