org.apache.commons.math3.special

## Class 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).
• ### Constructor Summary

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