Functions
constexpr double	Pi ()
	Pi constant.

constexpr double	GeVtoifm ()
	A constant to transform GeV into fm \(^{-1}\).

constexpr double	GeVtoifm2 ()
	A constant to transform GeV \(^{2}\) into fm \(^{-2}\).

constexpr double	GeVtoifm3 ()
	A constant to transform GeV \(^{3}\) into fm \(^{-3}\).

constexpr double	mnucleon ()
	Nucleon's mass. Value as in UrQMD.

constexpr double	mpion ()
	Pion's mass. Value as in UrQMD.

double	BesselI (int n, double x)
	Integer order modified Bessel function I_n(x)

double	BesselK (int n, double x)
	Integer order modified Bessel function K_n(x)

double	BesselI0 (double x)
	Modified Bessel function I_0(x)

double	BesselK0 (double x)
	Modified Bessel function K_0(x)

double	BesselI1 (double x)
	Modified Bessel function I_1(x)

double	BesselK1 (double x)
	Modified Bessel function K_1(x)

double	BesselJ0 (double x)
	Bessel function J0(x) for any real x.

double	BesselJ1 (double x)
	Bessel function J1(x) for any real x.

double	BesselY0 (double x)
	Bessel function Y0(x) for positive x.

double	BesselY1 (double x)
	Bessel function Y1(x) for positive x.

double	StruveH0 (double x)
	Struve function of order 0.

double	StruveH1 (double x)
	Struve function of order 1.

double	StruveL0 (double x)
	Modified Struve function of order 0.

double	StruveL1 (double x)
	Modified Struve function of order 1.

double	BesselK0exp (double x)
	Modified Bessel function K_0(x), divided by exponential factor.

double	BesselK1exp (double x)
	Modified Bessel function K_1(x), divided by exponential factor.

double	BesselKexp (int n, double x)
	Modified Bessel function K_n(x), divided by exponential factor.

double	BesselI0exp (double x)
	Modified Bessel function I_0(x), divided by exponential factor.

double	BesselI1exp (double x)
	Modified Bessel function I_1(x), divided by exponential factor.

double	BesselIexp (int n, double x)
	Modified Bessel function I_n(x), divided by exponential factor.

double	LogGamma (double x)
	Computes the logarithm of the Gamma function.

double	Gamma (double x)
	Computes the Gamma function.

template<typename T>
T	LambertW0 (T z)
	Computes the Lambert W function (0-branch) using Halley's method.

Function Documentation

◆ BesselI()

double thermalfist::xMath::BesselI	(	int	n,
		double	x )

Integer order modified Bessel function I_n(x)

Bessel and related special functions. Implementation of these special functions is adapted from the CERN-ROOT package: https://root.cern.ch/

Parameters

n	Order of the Bessel function
x	Argument of the Bessel function

Returns: Value of the Bessel function I_n(x)

Definition at line 192 of file xMath.cpp.

◆ BesselI0()

double thermalfist::xMath::BesselI0 ( double x )

Modified Bessel function I_0(x)

Parameters

x	Argument of the Bessel function

Returns: Value of the Bessel function I_0(x)

Definition at line 23 of file xMath.cpp.

◆ BesselI0exp()

double thermalfist::xMath::BesselI0exp ( double x )

Modified Bessel function I_0(x), divided by exponential factor.

Parameters

x	Argument of the Bessel function

Returns: Value of I_0(x) * exp(-x)

Definition at line 723 of file xMath.cpp.

◆ BesselI1()

double thermalfist::xMath::BesselI1 ( double x )

Modified Bessel function I_1(x)

Parameters

x	Argument of the Bessel function

Returns: Value of the Bessel function I_1(x)

Definition at line 91 of file xMath.cpp.

◆ BesselI1exp()

double thermalfist::xMath::BesselI1exp ( double x )

Modified Bessel function I_1(x), divided by exponential factor.

Parameters

x	Argument of the Bessel function

Returns: Value of I_1(x) * exp(-x)

Definition at line 755 of file xMath.cpp.

◆ BesselIexp()

double thermalfist::xMath::BesselIexp	(	int	n,
		double	x )

Modified Bessel function I_n(x), divided by exponential factor.

Parameters

n	Order of the Bessel function
x	Argument of the Bessel function

Returns: Value of I_n(x) * exp(-x)

Definition at line 791 of file xMath.cpp.

◆ BesselJ0()

double thermalfist::xMath::BesselJ0 ( double x )

Bessel function J0(x) for any real x.

Parameters

x	Argument of the Bessel function

Returns: Value of the Bessel function J0(x)

Definition at line 235 of file xMath.cpp.

◆ BesselJ1()

double thermalfist::xMath::BesselJ1 ( double x )

Bessel function J1(x) for any real x.

Parameters

x	Argument of the Bessel function

Returns: Value of the Bessel function J1(x)

Definition at line 271 of file xMath.cpp.

◆ BesselK()

double thermalfist::xMath::BesselK	(	int	n,
		double	x )

Integer order modified Bessel function K_n(x)

Parameters

n	Order of the Bessel function
x	Argument of the Bessel function

Returns: Value of the Bessel function K_n(x)

Definition at line 162 of file xMath.cpp.

◆ BesselK0()

double thermalfist::xMath::BesselK0 ( double x )

Modified Bessel function K_0(x)

Parameters

x	Argument of the Bessel function

Returns: Value of the Bessel function K_0(x)

Definition at line 55 of file xMath.cpp.

◆ BesselK0exp()

double thermalfist::xMath::BesselK0exp ( double x )

Modified Bessel function K_0(x), divided by exponential factor.

Parameters

x	Argument of the Bessel function

Returns: Value of K_0(x) * exp(x)

Definition at line 623 of file xMath.cpp.

◆ BesselK1()

double thermalfist::xMath::BesselK1 ( double x )

Modified Bessel function K_1(x)

Parameters

x	Argument of the Bessel function

Returns: Value of the Bessel function K_1(x)

Definition at line 127 of file xMath.cpp.

◆ BesselK1exp()

double thermalfist::xMath::BesselK1exp ( double x )

Modified Bessel function K_1(x), divided by exponential factor.

Parameters

x	Argument of the Bessel function

Returns: Value of K_1(x) * exp(x)

Definition at line 657 of file xMath.cpp.

◆ BesselKexp()

double thermalfist::xMath::BesselKexp	(	int	n,
		double	x )

Modified Bessel function K_n(x), divided by exponential factor.

Parameters

n	Order of the Bessel function
x	Argument of the Bessel function

Returns: Value of K_n(x) * exp(x)

Definition at line 693 of file xMath.cpp.

◆ BesselY0()

double thermalfist::xMath::BesselY0 ( double x )

Bessel function Y0(x) for positive x.

Parameters

x	Argument of the Bessel function (must be positive)

Returns: Value of the Bessel function Y0(x)

Definition at line 308 of file xMath.cpp.

◆ BesselY1()

double thermalfist::xMath::BesselY1 ( double x )

Bessel function Y1(x) for positive x.

Parameters

x	Argument of the Bessel function (must be positive)

Returns: Value of the Bessel function Y1(x)

Definition at line 343 of file xMath.cpp.

◆ Gamma()

double thermalfist::xMath::Gamma ( double x )

Computes the Gamma function.

Parameters

x	Argument of the function

Returns: Value of Gamma(x)

Definition at line 834 of file xMath.cpp.

◆ GeVtoifm()

double thermalfist::xMath::GeVtoifm ( )

constexpr

A constant to transform GeV into fm \(^{-1}\).

Definition at line 25 of file xMath.h.

◆ GeVtoifm2()

double thermalfist::xMath::GeVtoifm2 ( )

constexpr

A constant to transform GeV \(^{2}\) into fm \(^{-2}\).

Definition at line 28 of file xMath.h.

◆ GeVtoifm3()

double thermalfist::xMath::GeVtoifm3 ( )

constexpr

A constant to transform GeV \(^{3}\) into fm \(^{-3}\).

Definition at line 31 of file xMath.h.

◆ LambertW0()

template<typename T>

T thermalfist::xMath::LambertW0 ( T z )

Computes the Lambert W function (0-branch) using Halley's method.

The Lambert W function is the inverse function of ( f(W) = W e^W ). This implementation uses Halley's method to achieve the desired accuracy within 10 * epsilon, where epsilon is the machine precision. The initial guess for the iteration is z = 0.

Template Parameters

T	The type of the input value.

Parameters

z	The input value for which the Lambert W function is computed.

Returns: The computed value of the Lambert W function for the given input.

◆ LogGamma()

double thermalfist::xMath::LogGamma ( double x )

Computes the logarithm of the Gamma function.

Note that the functions Gamma and LogGamma are mutually dependent.

Parameters

x	Argument of the function

Returns: Value of log(Gamma(x))

Definition at line 954 of file xMath.cpp.

◆ mnucleon()

double thermalfist::xMath::mnucleon ( )

constexpr

Nucleon's mass. Value as in UrQMD.

Definition at line 34 of file xMath.h.

◆ mpion()

double thermalfist::xMath::mpion ( )

constexpr

Pion's mass. Value as in UrQMD.

Definition at line 37 of file xMath.h.

◆ Pi()

double thermalfist::xMath::Pi ( )

constexpr

Pi constant.

Definition at line 23 of file xMath.h.

◆ StruveH0()

double thermalfist::xMath::StruveH0 ( double x )

Struve function of order 0.

Parameters

x	Argument of the Struve function

Returns: Value of the Struve function H0(x)

Definition at line 380 of file xMath.cpp.

◆ StruveH1()

double thermalfist::xMath::StruveH1 ( double x )

Struve function of order 1.

Parameters

x	Argument of the Struve function

Returns: Value of the Struve function H1(x)

Definition at line 450 of file xMath.cpp.

◆ StruveL0()

double thermalfist::xMath::StruveL0 ( double x )

Modified Struve function of order 0.

Parameters

x	Argument of the modified Struve function

Returns: Value of the modified Struve function L0(x)

Definition at line 531 of file xMath.cpp.

◆ StruveL1()

double thermalfist::xMath::StruveL1 ( double x )

Modified Struve function of order 1.

Parameters

x	Argument of the modified Struve function

Returns: Value of the modified Struve function L1(x)

Definition at line 578 of file xMath.cpp.

Functions

Function Documentation

◆ BesselI()

◆ BesselI0()

◆ BesselI0exp()

◆ BesselI1()

◆ BesselI1exp()

◆ BesselIexp()

◆ BesselJ0()

◆ BesselJ1()

◆ BesselK()

◆ BesselK0()

◆ BesselK0exp()

◆ BesselK1()

◆ BesselK1exp()

◆ BesselKexp()

◆ BesselY0()

◆ BesselY1()

◆ Gamma()

◆ GeVtoifm()

◆ GeVtoifm2()

◆ GeVtoifm3()

◆ LambertW0()

◆ LogGamma()

◆ mnucleon()

◆ mpion()

◆ Pi()

◆ StruveH0()

◆ StruveH1()

◆ StruveL0()

◆ StruveL1()