Bessel (OpenGamma Strata Math API)

java.lang.Object
- com.opengamma.strata.math.impl.cern.Bessel

```
public class Bessel
extends Object
```
Bessel and Airy functions.

Field Summary

Fields
Modifier and Type	Field and Description
`protected static double[]`	`A_i0` Chebyshev coefficients for exp(-x) I0(x) in the interval [0,8].
`protected static double[]`	`A_i1` Chebyshev coefficients for exp(-x) I1(x) / x in the interval [0,8].
`protected static double[]`	`A_k0` COEFFICIENTS FOR METHODS k0, k0e *
`protected static double[]`	`A_k1` COEFFICIENTS FOR METHODS k1, k1e *
`protected static double[]`	`B_i0` Chebyshev coefficients for exp(-x) sqrt(x) I0(x) in the inverted interval [8,infinity].
`protected static double[]`	`B_i1`
`protected static double[]`	`B_k0`
`protected static double[]`	`B_k1`
`protected static double`	`big`
`protected static double`	`biginv`
`protected static double`	`LOGPI`
`protected static double`	`MACHEP`
`protected static double`	`MAXGAM`
`protected static double`	`MAXLOG`
`protected static double`	`MINLOG`
`protected static double`	`SQRTH`
`protected static double`	`SQTPI`

Constructor Summary

Constructors
Modifier Constructor and Description

protected Bessel()
Makes this class non instantiable, but still let's others inherit from it.

Constructors
Modifier	Constructor and Description
`protected`	`Bessel()` Makes this class non instantiable, but still let's others inherit from it.

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and Description
`static double`	`i0(double x)` Returns the modified Bessel function of order 0 of the argument.
`static double`	`i0e(double x)` Returns the exponentially scaled modified Bessel function of order 0 of the argument.
`static double`	`i1(double x)` Returns the modified Bessel function of order 1 of the argument.
`static double`	`i1e(double x)` Returns the exponentially scaled modified Bessel function of order 1 of the argument.
`static double`	`j0(double x)` Returns the Bessel function of the first kind of order 0 of the argument.
`static double`	`j1(double x)` Returns the Bessel function of the first kind of order 1 of the argument.
`static double`	`jn(int n, double x)` Returns the Bessel function of the first kind of order `n` of the argument.
`static double`	`k0(double x)` Returns the modified Bessel function of the third kind of order 0 of the argument.
`static double`	`k0e(double x)` Returns the exponentially scaled modified Bessel function of the third kind of order 0 of the argument.
`static double`	`k1(double x)` Returns the modified Bessel function of the third kind of order 1 of the argument.
`static double`	`k1e(double x)` Returns the exponentially scaled modified Bessel function of the third kind of order 1 of the argument.
`static double`	`kn(int nn, double x)` Returns the modified Bessel function of the third kind of order `nn` of the argument.
`static double`	`y0(double x)` Returns the Bessel function of the second kind of order 0 of the argument.
`static double`	`y1(double x)` Returns the Bessel function of the second kind of order 1 of the argument.
`static double`	`yn(int n, double x)` Returns the Bessel function of the second kind of order `n` of the argument.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - A_i0
```
protected static final double[] A_i0
```
    Chebyshev coefficients for exp(-x) I0(x) in the interval [0,8]. lim(x->0){ exp(-x) I0(x) } = 1.
  - B_i0
```
protected static final double[] B_i0
```
    Chebyshev coefficients for exp(-x) sqrt(x) I0(x) in the inverted interval [8,infinity]. lim(x->inf){ exp(-x) sqrt(x) I0(x) } = 1/sqrt(2pi).
  - A_i1
```
protected static final double[] A_i1
```
    Chebyshev coefficients for exp(-x) I1(x) / x in the interval [0,8]. lim(x->0){ exp(-x) I1(x) / x } = 1/2.
  - B_i1
```
protected static final double[] B_i1
```
  - A_k0
```
protected static final double[] A_k0
```
    COEFFICIENTS FOR METHODS k0, k0e *
  - B_k0
```
protected static final double[] B_k0
```
  - A_k1
```
protected static final double[] A_k1
```
    COEFFICIENTS FOR METHODS k1, k1e *
  - B_k1
```
protected static final double[] B_k1
```
  - MACHEP
```
protected static final double MACHEP
```
    See Also:
    
    Constant Field Values
  - MAXLOG
```
protected static final double MAXLOG
```
    See Also:
    
    Constant Field Values
  - MINLOG
```
protected static final double MINLOG
```
    See Also:
    
    Constant Field Values
  - MAXGAM
```
protected static final double MAXGAM
```
    See Also:
    
    Constant Field Values
  - SQTPI
```
protected static final double SQTPI
```
    See Also:
    
    Constant Field Values
  - SQRTH
```
protected static final double SQRTH
```
    See Also:
    
    Constant Field Values
  - LOGPI
```
protected static final double LOGPI
```
    See Also:
    
    Constant Field Values
  - big
```
protected static final double big
```
    See Also:
    
    Constant Field Values
  - biginv
```
protected static final double biginv
```
    See Also:
    
    Constant Field Values
- Constructor Detail
  - Bessel
```
protected Bessel()
```
    Makes this class non instantiable, but still let's others inherit from it.
- Method Detail
  - i0
```
public static double i0(double x)
                 throws ArithmeticException
```
    Returns the modified Bessel function of order 0 of the argument.
    The function is defined as i0(x) = j0( ix ).
    The range is partitioned into the two intervals [0,8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval.
    
    Parameters:
    
    x - the value to compute the bessel function of.
    
    Returns:
    
    result
    
    Throws:
    
    ArithmeticException - error
  - i0e
```
public static double i0e(double x)
                  throws ArithmeticException
```
    Returns the exponentially scaled modified Bessel function of order 0 of the argument.
    The function is defined as i0e(x) = exp(-|x|) j0( ix ).
    
    Parameters:
    
    x - the value to compute the bessel function of.
    
    Returns:
    
    result
    
    Throws:
    
    ArithmeticException - error
  - i1
```
public static double i1(double x)
                 throws ArithmeticException
```
    Returns the modified Bessel function of order 1 of the argument.
    The function is defined as i1(x) = -i j1( ix ).
    The range is partitioned into the two intervals [0,8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval.
    
    Parameters:
    
    x - the value to compute the bessel function of.
    
    Returns:
    
    result
    
    Throws:
    
    ArithmeticException - error
  - i1e
```
public static double i1e(double x)
                  throws ArithmeticException
```
    Returns the exponentially scaled modified Bessel function of order 1 of the argument.
    The function is defined as i1(x) = -i exp(-|x|) j1( ix ).
    
    Parameters:
    
    x - the value to compute the bessel function of.
    
    Returns:
    
    result
    
    Throws:
    
    ArithmeticException - error
  - j0
```
public static double j0(double x)
                 throws ArithmeticException
```
    Returns the Bessel function of the first kind of order 0 of the argument.
    
    Parameters:
    
    x - the value to compute the bessel function of.
    
    Returns:
    
    result
    
    Throws:
    
    ArithmeticException - error
  - j1
```
public static double j1(double x)
                 throws ArithmeticException
```
    Returns the Bessel function of the first kind of order 1 of the argument.
    
    Parameters:
    
    x - the value to compute the bessel function of.
    
    Returns:
    
    result
    
    Throws:
    
    ArithmeticException - error
  - jn
```
public static double jn(int n,
                        double x)
                 throws ArithmeticException
```
    Returns the Bessel function of the first kind of order n of the argument.
    
    Parameters:
    
    n - the order of the Bessel function.
    
    x - the value to compute the bessel function of.
    
    Returns:
    
    result
    
    Throws:
    
    ArithmeticException - error
  - k0
```
public static double k0(double x)
                 throws ArithmeticException
```
    Returns the modified Bessel function of the third kind of order 0 of the argument.
    The range is partitioned into the two intervals [0,8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval.
    
    Parameters:
    
    x - the value to compute the bessel function of.
    
    Returns:
    
    result
    
    Throws:
    
    ArithmeticException - error
  - k0e
```
public static double k0e(double x)
                  throws ArithmeticException
```
    Returns the exponentially scaled modified Bessel function of the third kind of order 0 of the argument.
    
    Parameters:
    
    x - the value to compute the bessel function of.
    
    Returns:
    
    result
    
    Throws:
    
    ArithmeticException - error
  - k1
```
public static double k1(double x)
                 throws ArithmeticException
```
    Returns the modified Bessel function of the third kind of order 1 of the argument.
    The range is partitioned into the two intervals [0,2] and (2, infinity). Chebyshev polynomial expansions are employed in each interval.
    
    Parameters:
    
    x - the value to compute the bessel function of.
    
    Returns:
    
    result
    
    Throws:
    
    ArithmeticException - error
  - k1e
```
public static double k1e(double x)
                  throws ArithmeticException
```
    Returns the exponentially scaled modified Bessel function of the third kind of order 1 of the argument.
    k1e(x) = exp(x) * k1(x).
    
    Parameters:
    
    x - the value to compute the bessel function of.
    
    Returns:
    
    result
    
    Throws:
    
    ArithmeticException - error
  - kn
```
public static double kn(int nn,
                        double x)
                 throws ArithmeticException
```
    Returns the modified Bessel function of the third kind of order nn of the argument.
    The range is partitioned into the two intervals [0,9.55] and (9.55, infinity). An ascending power series is used in the low range, and an asymptotic expansion in the high range.
    
    Parameters:
    
    nn - the order of the Bessel function.
    
    x - the value to compute the bessel function of.
    
    Returns:
    
    result
    
    Throws:
    
    ArithmeticException - error
  - y0
```
public static double y0(double x)
                 throws ArithmeticException
```
    Returns the Bessel function of the second kind of order 0 of the argument.
    
    Parameters:
    
    x - the value to compute the bessel function of.
    
    Returns:
    
    result
    
    Throws:
    
    ArithmeticException - error
  - y1
```
public static double y1(double x)
                 throws ArithmeticException
```
    Returns the Bessel function of the second kind of order 1 of the argument.
    
    Parameters:
    
    x - the value to compute the bessel function of.
    
    Returns:
    
    result
    
    Throws:
    
    ArithmeticException - error
  - yn
```
public static double yn(int n,
                        double x)
                 throws ArithmeticException
```
    Returns the Bessel function of the second kind of order n of the argument.
    
    Parameters:
    
    n - the order of the Bessel function.
    
    x - the value to compute the bessel function of.
    
    Returns:
    
    result
    
    Throws:
    
    ArithmeticException - error

Copyright 2009-Present by OpenGamma Inc. and individual contributors
Apache v2 licensed
Additional documentation can be found at strata.opengamma.io.

Class Bessel

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

A_i0

B_i0

A_i1

B_i1

A_k0

B_k0

A_k1

B_k1

MACHEP

MAXLOG

MINLOG

MAXGAM

SQTPI

SQRTH

LOGPI

big

biginv

Constructor Detail

Bessel

Method Detail

i0

i0e

i1

i1e

j0

j1

jn

k0

k0e

k1

k1e

kn

y0

y1

yn