graph

Class SpecialFunction

java.lang.Object

graph.SpecialFunction

public final class SpecialFunction
extends Object

This class contains physical constants and special functions not found in the java.lang.Math class. Like the java.lang.Math class this class is final and cannot be subclassed. All physical constants are in cgs units.

NOTE: These special functions do not necessarily use the fastest or most accurate algorithms.

Field Summary

Fields

Modifier and Type	Field and Description
static double	AU Astronomical Unit (radius of the Earth's orbit).
static double	AVOGADRO Avogadro Number.
static double	BOLTZMAN Boltzman Constant.
static double	ECHARGE Elementary Charge.
static double	EMASS Electron Mass.
static double	GASCONSTANT Gas Constant.
static double	GRAV Gravitational Constant.
static double	GRAVACC Gravitational Acceleration at the Earths surface.
static double	LIGHTSPEED Speed of Light in a Vacuum.
static double	PLANCK Planck constant.
static double	PMASS Proton Mass.
static double	SOLARFLUX Solar Flux.
static double	SOLARLUM Solar Luminosity.
static double	SOLARMASS Solar Mass.
static double	SOLARRADIUS Solar Radius.
static double	STEFANBOLTZ Stefan-Boltzman Constant.

Method Summary

Modifier and Type	Method and Description
static double	acosh(double x)
static double	asinh(double xx)
static double	atanh(double x)
static double	chisq(double df, double x) Returns the area under the left hand tail (from 0 to x) of the Chi square probability density function with v degrees of freedom.
static double	chisqc(double df, double x) Returns the area under the right hand tail (from x to infinity) of the Chi square probability density function with v degrees of freedom:
static double	cosh(double x)
static double	erf(double x)
static double	erfc(double a)
static double	fac(double x)
static int	fac(int j)
static double	gamma(double x)
static double	ibeta(double aa, double bb, double xx)
static double	igam(double a, double x)
static double	igamc(double a, double x)
static double	j0(double x)
static double	j1(double x)
static double	jn(int n, double x)
static double	log10(double x)
static double	normal(double a)
static double	poisson(int k, double x) Returns the sum of the first k terms of the Poisson distribution.
static double	poissonc(int k, double x) Returns the sum of the terms k+1 to infinity of the Poisson distribution.
static double	sinh(double x)
static double	tanh(double x)
static double	y0(double x)
static double	y1(double x)
static double	yn(int n, double x)

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

BOLTZMAN

public static final double BOLTZMAN

Boltzman Constant. Units erg/deg(K)

See Also:

Constant Field Values

ECHARGE

public static final double ECHARGE

Elementary Charge. Units statcoulomb

See Also:

Constant Field Values

EMASS

public static final double EMASS

Electron Mass. Units g

See Also:

Constant Field Values

PMASS

public static final double PMASS

Proton Mass. Units g

See Also:

Constant Field Values

GRAV

public static final double GRAV

Gravitational Constant. Units dyne-cm^2/g^2

See Also:

Constant Field Values

PLANCK

public static final double PLANCK

Planck constant. Units erg-sec

See Also:

Constant Field Values

LIGHTSPEED

public static final double LIGHTSPEED

Speed of Light in a Vacuum. Units cm/sec

See Also:

Constant Field Values

STEFANBOLTZ

public static final double STEFANBOLTZ

Stefan-Boltzman Constant. Units erg/cm^2-sec-deg^4

See Also:

Constant Field Values

AVOGADRO

public static final double AVOGADRO

Avogadro Number. Units 1/mol

See Also:

Constant Field Values

GASCONSTANT

public static final double GASCONSTANT

Gas Constant. Units erg/deg-mol

See Also:

Constant Field Values

GRAVACC

public static final double GRAVACC

Gravitational Acceleration at the Earths surface. Units cm/sec^2

See Also:

Constant Field Values

SOLARMASS

public static final double SOLARMASS

Solar Mass. Units g

See Also:

Constant Field Values

SOLARRADIUS

public static final double SOLARRADIUS

Solar Radius. Units cm

See Also:

Constant Field Values

SOLARLUM

public static final double SOLARLUM

Solar Luminosity. Units erg/sec

See Also:

Constant Field Values

SOLARFLUX

public static final double SOLARFLUX

Solar Flux. Units erg/cm^2-sec

See Also:

Constant Field Values

AU

public static final double AU

Astronomical Unit (radius of the Earth's orbit). Units cm

See Also:

Constant Field Values

Method Detail

log10

public static double log10(double x)
                    throws ArithmeticException

Parameters:

x - a double value

Returns:

The log₁₀

Throws:

ArithmeticException

cosh

public static double cosh(double x)
                   throws ArithmeticException

Parameters:

x - a double value

Returns:

the hyperbolic cosine of the argument

Throws:

ArithmeticException

sinh

public static double sinh(double x)
                   throws ArithmeticException

Parameters:

x - a double value

Returns:

the hyperbolic sine of the argument

Throws:

ArithmeticException

tanh

public static double tanh(double x)
                   throws ArithmeticException

Parameters:

x - a double value

Returns:

the hyperbolic tangent of the argument

Throws:

ArithmeticException

acosh

public static double acosh(double x)
                    throws ArithmeticException

Parameters:

x - a double value

Returns:

the hyperbolic arc cosine of the argument

Throws:

ArithmeticException

asinh

public static double asinh(double xx)
                    throws ArithmeticException

Parameters:

x - a double value

Returns:

the hyperbolic arc sine of the argument

Throws:

ArithmeticException

atanh

public static double atanh(double x)
                    throws ArithmeticException

Parameters:

x - a double value

Returns:

the hyperbolic arc tangent of the argument

Throws:

ArithmeticException

j0

public static double j0(double x)
                 throws ArithmeticException

Parameters:

x - a double value

Returns:

the Bessel function of order 0 of the argument.

Throws:

ArithmeticException

j1

public static double j1(double x)
                 throws ArithmeticException

Parameters:

x - a double value

Returns:

the Bessel function of order 1 of the argument.

Throws:

ArithmeticException

jn

public static double jn(int n,
                        double x)
                 throws ArithmeticException

Parameters:

n - integer order

x - a double value

Returns:

the Bessel function of order n of the argument.

Throws:

ArithmeticException

y0

public static double y0(double x)
                 throws ArithmeticException

Parameters:

x - a double value

Returns:

the Bessel function of the second kind, of order 0 of the argument.

Throws:

ArithmeticException

y1

public static double y1(double x)
                 throws ArithmeticException

Parameters:

x - a double value

Returns:

the Bessel function of the second kind, of order 1 of the argument.

Throws:

ArithmeticException

yn

public static double yn(int n,
                        double x)
                 throws ArithmeticException

Parameters:

n - integer order

x - a double value

Returns:

the Bessel function of the second kind, of order n of the argument.

Throws:

ArithmeticException

fac

public static double fac(double x)
                  throws ArithmeticException

Parameters:

x - a double value

Returns:

the factorial of the argument

Throws:

ArithmeticException

fac

public static int fac(int j)
               throws ArithmeticException

Parameters:

x - an integer value

Returns:

the factorial of the argument

Throws:

ArithmeticException

gamma

public static double gamma(double x)
                    throws ArithmeticException

Parameters:

x - a double value

Returns:

the Gamma function of the value.

Converted to Java from
Cephes Math Library Release 2.2: July, 1992
Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140

Throws:

ArithmeticException

igamc

public static double igamc(double a,
                           double x)
                    throws ArithmeticException

Parameters:

a - double value

x - double value

Returns:

the Complemented Incomplete Gamma function.

Converted to Java from
Cephes Math Library Release 2.2: July, 1992
Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140

Throws:

ArithmeticException

igam

public static double igam(double a,
                          double x)
                   throws ArithmeticException

Parameters:

a - double value

x - double value

Returns:

the Incomplete Gamma function.

Converted to Java from
Cephes Math Library Release 2.2: July, 1992
Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140

Throws:

ArithmeticException

chisq

public static double chisq(double df,
                           double x)
                    throws ArithmeticException

Returns the area under the left hand tail (from 0 to x) of the Chi square probability density function with v degrees of freedom.

Parameters:

df - degrees of freedom

x - double value

Returns:

the Chi-Square function.

Throws:

ArithmeticException

chisqc

public static double chisqc(double df,
                            double x)
                     throws ArithmeticException

Returns the area under the right hand tail (from x to infinity) of the Chi square probability density function with v degrees of freedom:

Parameters:

df - degrees of freedom

x - double value

Returns:

the Chi-Square function.

Throws:

ArithmeticException

poisson

public static double poisson(int k,
                             double x)
                      throws ArithmeticException

Returns the sum of the first k terms of the Poisson distribution.

Parameters:

k - number of terms

x - double value

Throws:

ArithmeticException

poissonc

public static double poissonc(int k,
                              double x)
                       throws ArithmeticException

Returns the sum of the terms k+1 to infinity of the Poisson distribution.

Parameters:

k - start

x - double value

Throws:

ArithmeticException

normal

public static double normal(double a)
                     throws ArithmeticException

Parameters:

a - double value

Returns:

The area under the Gaussian probability density function, integrated from minus infinity to x:

Throws:

ArithmeticException

erfc

public static double erfc(double a)
                   throws ArithmeticException

Parameters:

a - double value

Returns:

The complementary Error function

Converted to Java from
Cephes Math Library Release 2.2: July, 1992
Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140

Throws:

ArithmeticException

erf

public static double erf(double x)
                  throws ArithmeticException

Parameters:

a - double value

Returns:

The Error function

Converted to Java from
Cephes Math Library Release 2.2: July, 1992
Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140

Throws:

ArithmeticException

ibeta

public static double ibeta(double aa,
                           double bb,
                           double xx)
                    throws ArithmeticException

Parameters:

aa - double value

bb - double value

xx - double value

Returns:

The Incomplete Beta Function evaluated from zero to xx.

Converted to Java from
Cephes Math Library Release 2.3: July, 1995
Copyright 1984, 1995 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140

Throws:

ArithmeticException