Class SpecialFunctions
- java.lang.Object
-
- org.mariuszgromada.math.mxparser.mathcollection.SpecialFunctions
-
public final class SpecialFunctions extends Object
SpecialFunctions - special (non-elementary functions).- Version:
- 5.1.0
- Author:
- Mariusz Gromada
MathParser.org - mXparser project page
mXparser on GitHub
INFIMA place to purchase a commercial MathParser.org-mXparser software license
info@mathparser.org
ScalarMath.org - a powerful math engine and math scripting language
Scalar Lite
Scalar Pro
MathSpace.pl
Buy me a cup of coffee via donation
or support me purchasing the license via ORDER Page , or INFIMA online store
-
-
Constructor Summary
Constructors Constructor Description SpecialFunctions()
-
Method Summary
All Methods Static Methods Concrete Methods Modifier and Type Method Description static double
beta(double x, double y)
Beta special functionstatic double
diGamma(double x)
Digamma function as the logarithmic derivative of the Gamma special functionstatic double
erf(double x)
Calculates the error functionstatic double
erfc(double x)
Calculates the complementary error function.static double
erfcInv(double z)
Calculates the complementary inverse error function evaluated at x.static double
erfInv(double x)
Calculates the inverse error function evaluated at x.static double
exponentialIntegralEi(double x)
Exponential integral function Ei(x)static double
gamma(double x)
Real valued Gamma functionstatic double
hypergeometricF(double a, double b, double c, double z, double maxIterations, double precision)
The Gaussian or ordinary hypergeometric special functionstatic double
incompleteBeta(double a, double b, double x)
Log Incomplete Beta special functionstatic double
incompleteGammaLower(double s, double x)
Incomplete lower gamma functionstatic double
incompleteGammaUpper(double s, double x)
Incomplete upper gamma functionstatic double
inverseRegularizedBeta(double a, double b, double p)
Inerse regularized incomplete Beta special functionstatic double
inverseRegularizedGammaLowerP(double a, double p)
Inverse of regularized lower gamma function 'P'static double
lambertW(double x, double branch)
Real-valued Lambert-W function approximation.static double
lanchosGamma(double x)
Gamma function implementation based on Lanchos approximation algorithmstatic double
logarithmicIntegralLi(double x)
Logarithmic integral function li(x)static double
logBeta(double x, double y)
Log Beta special functionstatic double
logGamma(double x)
Real valued log gamma function.static double
offsetLogarithmicIntegralLi(double x)
Offset logarithmic integral function Li(x)static double
regularizedBeta(double a, double b, double x)
Regularized incomplete Beta special functionstatic double
regularizedGammaLowerP(double s, double x)
Regularized lower gamma function 'P'static double
regularizedGammaUpperQ(double s, double x)
Regularized upper gamma function 'Q'static double
sgnGamma(double x)
Signum from the real valued gamma function.
-
-
-
Method Detail
-
exponentialIntegralEi
public static double exponentialIntegralEi(double x)
Exponential integral function Ei(x)- Parameters:
x
- Point at which function will be evaluated.- Returns:
- Exponential integral function Ei(x)
-
logarithmicIntegralLi
public static double logarithmicIntegralLi(double x)
Logarithmic integral function li(x)- Parameters:
x
- Point at which function will be evaluated.- Returns:
- Logarithmic integral function li(x)
-
offsetLogarithmicIntegralLi
public static double offsetLogarithmicIntegralLi(double x)
Offset logarithmic integral function Li(x)- Parameters:
x
- Point at which function will be evaluated.- Returns:
- Offset logarithmic integral function Li(x)
-
erf
public static double erf(double x)
Calculates the error function- Parameters:
x
- Point at which function will be evaluated.- Returns:
- Error function erf(x)
-
erfc
public static double erfc(double x)
Calculates the complementary error function.- Parameters:
x
- Point at which function will be evaluated.- Returns:
- Complementary error function erfc(x)
-
erfInv
public static double erfInv(double x)
Calculates the inverse error function evaluated at x.- Parameters:
x
- Point at which function will be evaluated.- Returns:
- Inverse error function erfInv(x)
-
erfcInv
public static double erfcInv(double z)
Calculates the complementary inverse error function evaluated at x.- Parameters:
z
- Point at which function will be evaluated.- Returns:
- Inverse of complementary inverse error function erfcInv(x)
-
gamma
public static double gamma(double x)
Real valued Gamma function- Parameters:
x
- Argument value- Returns:
- Returns gamma function value.
-
lanchosGamma
public static double lanchosGamma(double x)
Gamma function implementation based on Lanchos approximation algorithm- Parameters:
x
- Function parameter- Returns:
- Gamma function value (Lanchos approx).
-
logGamma
public static double logGamma(double x)
Real valued log gamma function.- Parameters:
x
- Argument value- Returns:
- Returns log value from gamma function.
-
sgnGamma
public static double sgnGamma(double x)
Signum from the real valued gamma function.- Parameters:
x
- Argument value- Returns:
- Returns signum of the gamma(x)
-
regularizedGammaLowerP
public static double regularizedGammaLowerP(double s, double x)
Regularized lower gamma function 'P'- Parameters:
s
- Argument valuex
- Argument value- Returns:
- Value of the regularized lower gamma function 'P'.
-
inverseRegularizedGammaLowerP
public static double inverseRegularizedGammaLowerP(double a, double p)
Inverse of regularized lower gamma function 'P'- Parameters:
a
- Argument valuep
- Argument value- Returns:
- Value of the inverse regularized lower gamma function 'P'.
-
incompleteGammaLower
public static double incompleteGammaLower(double s, double x)
Incomplete lower gamma function- Parameters:
s
- Argument valuex
- Argument value- Returns:
- Value of the incomplete lower gamma function.
-
regularizedGammaUpperQ
public static double regularizedGammaUpperQ(double s, double x)
Regularized upper gamma function 'Q'- Parameters:
s
- Argument valuex
- Argument value- Returns:
- Value of the regularized upper gamma function 'Q'.
-
incompleteGammaUpper
public static double incompleteGammaUpper(double s, double x)
Incomplete upper gamma function- Parameters:
s
- Argument valuex
- Argument value- Returns:
- Value of the incomplete upper gamma function.
-
diGamma
public static double diGamma(double x)
Digamma function as the logarithmic derivative of the Gamma special function- Parameters:
x
- Argument value- Returns:
- Approximated value of the digamma function.
-
logBeta
public static double logBeta(double x, double y)
Log Beta special function- Parameters:
x
- Argument valuey
- Argument value- Returns:
- Return logBeta special function (for positive x and positive y)
-
beta
public static double beta(double x, double y)
Beta special function- Parameters:
x
- Argument valuey
- Argument value- Returns:
- Return Beta special function (for positive x and positive y)
-
incompleteBeta
public static double incompleteBeta(double a, double b, double x)
Log Incomplete Beta special function- Parameters:
a
- Argument valueb
- Argument valuex
- Argument value- Returns:
- Return incomplete Beta special function for positive a and positive b and x between 0 and 1
-
regularizedBeta
public static double regularizedBeta(double a, double b, double x)
Regularized incomplete Beta special function- Parameters:
a
- Argument valueb
- Argument valuex
- Argument value- Returns:
- Return incomplete Beta special function for positive a and positive b and x between 0 and 1
-
inverseRegularizedBeta
public static double inverseRegularizedBeta(double a, double b, double p)
Inerse regularized incomplete Beta special function- Parameters:
a
- Argument valueb
- Argument valuep
- Argument value- Returns:
- Return inverse incomplete Beta special function for positive a and positive b and x between 0 and 1
-
lambertW
public static double lambertW(double x, double branch)
Real-valued Lambert-W function approximation.- Parameters:
x
- Point at which function will be approximatedbranch
- Branch id, 0 for principal branch, -1 for the other branch- Returns:
- Principal branch for x greater or equal than -1/e, otherwise Double.NaN. Minus 1 branch for x greater or equal than -1/e and lower than 0, otherwise Double.NaN.
-
hypergeometricF
public static double hypergeometricF(double a, double b, double c, double z, double maxIterations, double precision)
The Gaussian or ordinary hypergeometric special function- Parameters:
a
- Argument valueb
- Argument valuec
- Argument valuez
- Argument valuemaxIterations
- Stop conditionprecision
- Stop condition- Returns:
- Returns hypergeometric special function approximation
-
-