cern.jet.math

## Class Bessel

• ```public class Bessel
extends Constants```
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`
• ### Fields inherited from class cern.jet.math.Constants

`big, biginv, LOGPI, MACHEP, MAXGAM, MAXLOG, MINLOG, SQRTH, SQTPI`
• ### Constructor Summary

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

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`
• ### 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.
Throws:
`ArithmeticException`
• #### 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.
Throws:
`ArithmeticException`
• #### 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.
Throws:
`ArithmeticException`
• #### 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.
Throws:
`ArithmeticException`
• #### 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.
Throws:
`ArithmeticException`
• #### 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.
Throws:
`ArithmeticException`
• #### 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.
Throws:
`ArithmeticException`
• #### 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.
Throws:
`ArithmeticException`
• #### 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.
Throws:
`ArithmeticException`
• #### 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.
Throws:
`ArithmeticException`
• #### 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.
Throws:
`ArithmeticException`
• #### 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.
Throws:
`ArithmeticException`
• #### 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.
Throws:
`ArithmeticException`
• #### 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.
Throws:
`ArithmeticException`
• #### 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.
Throws:
`ArithmeticException`