BesselJ (Apache Commons Math 3.6.1 API)

java.lang.Object
- org.apache.commons.math3.special.BesselJ

All Implemented Interfaces:

UnivariateFunction
```
public class BesselJ
extends Object
implements UnivariateFunction
```
This class provides computation methods related to Bessel functions of the first kind. Detailed descriptions of these functions are available in Wikipedia, Abrabowitz and Stegun (Ch. 9-11), and DLMF (Ch. 10).
This implementation is based on the rjbesl Fortran routine at Netlib.

From the Fortran code:

This program is based on a program written by David J. Sookne (2) that computes values of the Bessel functions J or I of real argument and integer order. Modifications include the restriction of the computation to the J Bessel function of non-negative real argument, the extension of the computation to arbitrary positive order, and the elimination of most underflow.

References:
- "A Note on Backward Recurrence Algorithms," Olver, F. W. J., and Sookne, D. J., Math. Comp. 26, 1972, pp 941-947.
- "Bessel Functions of Real Argument and Integer Order," Sookne, D. J., NBS Jour. of Res. B. 77B, 1973, pp 125-132.
Since:

3.4

Nested Class Summary

Nested Classes
Modifier and Type Class and Description

static class BesselJ.BesselJResult
Encapsulates the results returned by rjBesl(double, double, int).

Nested Classes
Modifier and Type	Class and Description
`static class`	`BesselJ.BesselJResult` Encapsulates the results returned by `rjBesl(double, double, int)`.

Constructor Summary

Constructors
Constructor and Description

BesselJ(double order)
Create a new BesselJ with the given order.

Constructors
Constructor and Description
`BesselJ(double order)` Create a new BesselJ with the given order.

Method Summary

Methods
Modifier and Type	Method and Description
`static BesselJ.BesselJResult`	`rjBesl(double x, double alpha, int nb)` Calculates Bessel functions \(J_{n+alpha}(x)\) for non-negative argument x, and non-negative order n + alpha.
`double`	`value(double x)` Returns the value of the constructed Bessel function of the first kind, for the passed argument.
`static double`	`value(double order, double x)` Returns the first Bessel function, \(J_{order}(x)\).

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

- Constructor Detail
  - BesselJ
```
public BesselJ(double order)
```
    Create a new BesselJ with the given order.
    
    Parameters:
    order - order of the function computed when using value(double).
- Method Detail
  - value
```
public double value(double x)
             throws MathIllegalArgumentException,
                    ConvergenceException
```
    Returns the value of the constructed Bessel function of the first kind, for the passed argument.
    
    Specified by:
    
    value in interface UnivariateFunction
    
    Parameters:
    x - Argument
    
    Returns:
    Value of the Bessel function at x
    
    Throws:
    
    MathIllegalArgumentException - if x is too large relative to order
    
    ConvergenceException - if the algorithm fails to converge
  - value
```
public static double value(double order,
           double x)
                    throws MathIllegalArgumentException,
                           ConvergenceException
```
    Returns the first Bessel function, \(J_{order}(x)\).
    
    Parameters:
    order - Order of the Bessel function
    x - Argument
    
    Returns:
    Value of the Bessel function of the first kind, \(J_{order}(x)\)
    
    Throws:
    
    MathIllegalArgumentException - if x is too large relative to order
    
    ConvergenceException - if the algorithm fails to converge
  - rjBesl
```
public static BesselJ.BesselJResult rjBesl(double x,
                           double alpha,
                           int nb)
```
    Calculates Bessel functions \(J_{n+alpha}(x)\) for non-negative argument x, and non-negative order n + alpha.
    Before using the output vector, the user should check that nVals = nb, i.e., all orders have been calculated to the desired accuracy. See BesselResult class javadoc for details on return values.
    
    Parameters:
    x - non-negative real argument for which J's are to be calculated
    alpha - fractional part of order for which J's or exponentially scaled J's (\(J\cdot e^{x}\)) are to be calculated. 0 <= alpha < 1.0.
    nb - integer number of functions to be calculated, nb > 0. The first function calculated is of order alpha, and the last is of order nb - 1 + alpha.
    
    Returns:
    BesselJResult a vector of the functions \(J_{alpha}(x)\) through \(J_{nb-1+alpha}(x)\), or the corresponding exponentially scaled functions and an integer output variable indicating possible errors

Class BesselJ

Nested Class Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

BesselJ

Method Detail

value

value

rjBesl