IDL Analyst Reference Guide: Special Functions

IMSL_BESSJ

The IMSL_BESSJ function evaluates a Bessel function of the first kind with real order and real or complex parameters.

Syntax

Result = IMSL_BESSJ(order, z [, /DOUBLE] [, SEQUENCE=value])

Return Value

The desired value of the Bessel function.

Arguments

order

Real parameter specifying the desired order. The argument order must be greater than –1/2.

z

Real or complex parameter for which the Bessel function is to be evaluated.

Keywords

DOUBLE

If present and nonzero, double precision is used.

SEQUENCE

If present and nonzero, a one-dimensional array of length n containing the values of the Bessel function through the series is returned by IMSL_BESSJ, where n = NELEMENTS(SEQUENCE). The i-th element of this array is the Bessel function of order (order + i) at z for i = 0, ... (n – 1).

Discussion

The IMSL_BESSJ function evaluates a Bessel function of the first kind with real order and real or complex parameters. The data type of the returned value is always complex.

The Bessel function, J_v(z), is defined as follows:

for:

This function is based on the code BESSCC of Barnett (1981) and Thompson and Barnett (1987). This code computes J_v(z) from the modified Bessel function I_v(z), using the following relation with:

Example

In this example, J_{0.3 + v–1}(1.2 + 0.5i), v = 1, ..., 4 is computed and printed.

z = COMPLEX(1.2, .5)  
FOR i = 0, 3 DO PM, IMSL_BESSJ(i + .3, z)  
   (   0.773756, -0.106925)  
   (   0.400001,  0.158598)  
   (  0.0867063, 0.0920276)  
   ( 0.00844932, 0.0239868)  
PM, IMSL_BESSJ(.3, z, Sequence = 4), Title = 'With SEQUENCE:'  
With SEQUENCE:  
   (   0.773756, -0.106925)  
   (   0.400001,  0.158598)  
   (  0.0867063, 0.0920276)  
   ( 0.00844932, 0.0239868)