## org.mbari.siam.moos.utils.chart.graph Class SpecialFunction

```java.lang.Object
org.mbari.siam.moos.utils.chart.graph.SpecialFunction
```

`public final class SpecialFunctionextends java.lang.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.

Version:
\$Revision: 1.2 \$, \$Date: 2011/08/17 19:09:20 \$
Author:
Leigh Brookshaw

Field Summary
`static double` `AU`
Astronomical Unit (radius of the Earth's orbit).
`static double` `AVOGADRO`
`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`
`static double` `STEFANBOLTZ`
Stefan-Boltzman Constant.

Method Summary
`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
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Field Detail

### BOLTZMAN

`public static final double BOLTZMAN`
Boltzman Constant. Units erg/deg(K)

Constant Field Values

### ECHARGE

`public static final double ECHARGE`
Elementary Charge. Units statcoulomb

Constant Field Values

### EMASS

`public static final double EMASS`
Electron Mass. Units g

Constant Field Values

### PMASS

`public static final double PMASS`
Proton Mass. Units g

Constant Field Values

### GRAV

`public static final double GRAV`
Gravitational Constant. Units dyne-cm^2/g^2

Constant Field Values

### PLANCK

`public static final double PLANCK`
Planck constant. Units erg-sec

Constant Field Values

### LIGHTSPEED

`public static final double LIGHTSPEED`
Speed of Light in a Vacuum. Units cm/sec

Constant Field Values

### STEFANBOLTZ

`public static final double STEFANBOLTZ`
Stefan-Boltzman Constant. Units erg/cm^2-sec-deg^4

Constant Field Values

`public static final double AVOGADRO`

Constant Field Values

### GASCONSTANT

`public static final double GASCONSTANT`
Gas Constant. Units erg/deg-mol

Constant Field Values

### GRAVACC

`public static final double GRAVACC`
Gravitational Acceleration at the Earths surface. Units cm/sec^2

Constant Field Values

### SOLARMASS

`public static final double SOLARMASS`
Solar Mass. Units g

Constant Field Values

`public static final double SOLARRADIUS`

Constant Field Values

### SOLARLUM

`public static final double SOLARLUM`
Solar Luminosity. Units erg/sec

Constant Field Values

### SOLARFLUX

`public static final double SOLARFLUX`
Solar Flux. Units erg/cm^2-sec

Constant Field Values

### AU

`public static final double AU`
Astronomical Unit (radius of the Earth's orbit). Units cm

Constant Field Values
Method Detail

### log10

```public static double log10(double x)
throws java.lang.ArithmeticException```
Parameters:
`x` - a double value
Returns:
The log10
Throws:
`java.lang.ArithmeticException`

### cosh

```public static double cosh(double x)
throws java.lang.ArithmeticException```
Parameters:
`x` - a double value
Returns:
the hyperbolic cosine of the argument
Throws:
`java.lang.ArithmeticException`

### sinh

```public static double sinh(double x)
throws java.lang.ArithmeticException```
Parameters:
`x` - a double value
Returns:
the hyperbolic sine of the argument
Throws:
`java.lang.ArithmeticException`

### tanh

```public static double tanh(double x)
throws java.lang.ArithmeticException```
Parameters:
`x` - a double value
Returns:
the hyperbolic tangent of the argument
Throws:
`java.lang.ArithmeticException`

### acosh

```public static double acosh(double x)
throws java.lang.ArithmeticException```
Parameters:
`x` - a double value
Returns:
the hyperbolic arc cosine of the argument
Throws:
`java.lang.ArithmeticException`

### asinh

```public static double asinh(double xx)
throws java.lang.ArithmeticException```
Parameters:
`xx` - a double value
Returns:
the hyperbolic arc sine of the argument
Throws:
`java.lang.ArithmeticException`

### atanh

```public static double atanh(double x)
throws java.lang.ArithmeticException```
Parameters:
`x` - a double value
Returns:
the hyperbolic arc tangent of the argument
Throws:
`java.lang.ArithmeticException`

### j0

```public static double j0(double x)
throws java.lang.ArithmeticException```
Parameters:
`x` - a double value
Returns:
the Bessel function of order 0 of the argument.
Throws:
`java.lang.ArithmeticException`

### j1

```public static double j1(double x)
throws java.lang.ArithmeticException```
Parameters:
`x` - a double value
Returns:
the Bessel function of order 1 of the argument.
Throws:
`java.lang.ArithmeticException`

### jn

```public static double jn(int n,
double x)
throws java.lang.ArithmeticException```
Parameters:
`n` - integer order
`x` - a double value
Returns:
the Bessel function of order n of the argument.
Throws:
`java.lang.ArithmeticException`

### y0

```public static double y0(double x)
throws java.lang.ArithmeticException```
Parameters:
`x` - a double value
Returns:
the Bessel function of the second kind, of order 0 of the argument.
Throws:
`java.lang.ArithmeticException`

### y1

```public static double y1(double x)
throws java.lang.ArithmeticException```
Parameters:
`x` - a double value
Returns:
the Bessel function of the second kind, of order 1 of the argument.
Throws:
`java.lang.ArithmeticException`

### yn

```public static double yn(int n,
double x)
throws java.lang.ArithmeticException```
Parameters:
`n` - integer order
`x` - a double value
Returns:
the Bessel function of the second kind, of order n of the argument.
Throws:
`java.lang.ArithmeticException`

### fac

```public static double fac(double x)
throws java.lang.ArithmeticException```
Parameters:
`x` - a double value
Returns:
the factorial of the argument
Throws:
`java.lang.ArithmeticException`

### fac

```public static int fac(int j)
throws java.lang.ArithmeticException```
Parameters:
`j` - an integer value
Returns:
the factorial of the argument
Throws:
`java.lang.ArithmeticException`

### gamma

```public static double gamma(double x)
throws java.lang.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:
`java.lang.ArithmeticException`

### igamc

```public static double igamc(double a,
double x)
throws java.lang.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:
`java.lang.ArithmeticException`

### igam

```public static double igam(double a,
double x)
throws java.lang.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:
`java.lang.ArithmeticException`

### chisq

```public static double chisq(double df,
double x)
throws java.lang.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:
`java.lang.ArithmeticException`

### chisqc

```public static double chisqc(double df,
double x)
throws java.lang.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:
`java.lang.ArithmeticException`

### poisson

```public static double poisson(int k,
double x)
throws java.lang.ArithmeticException```
Returns the sum of the first k terms of the Poisson distribution.

Parameters:
`k` - number of terms
`x` - double value
Throws:
`java.lang.ArithmeticException`

### poissonc

```public static double poissonc(int k,
double x)
throws java.lang.ArithmeticException```
Returns the sum of the terms k+1 to infinity of the Poisson distribution.

Parameters:
`k` - start
`x` - double value
Throws:
`java.lang.ArithmeticException`

### normal

```public static double normal(double a)
throws java.lang.ArithmeticException```
Parameters:
`a` - double value
Returns:
The area under the Gaussian probability density function, integrated from minus infinity to x:
Throws:
`java.lang.ArithmeticException`

### erfc

```public static double erfc(double a)
throws java.lang.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:
`java.lang.ArithmeticException`

### erf

```public static double erf(double x)
throws java.lang.ArithmeticException```
Parameters:
`x` - 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:
`java.lang.ArithmeticException`

### ibeta

```public static double ibeta(double aa,
double bb,
double xx)
throws java.lang.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:
`java.lang.ArithmeticException`