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

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, Jv>(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 Jv(z) from the modified Bessel function Iv(z), using the following relation with:

## Example

In this example, J0.3 + 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:' `

IDL prints:

`With SEQUENCE:`
`  (  0.773756,   -0.106925)`
`  (  0.400001,    0.158598)`
`  ( 0.0867063,   0.0920276)`
`  ( 0.00844932,  0.0239868)`

## Syntax

Result = IMSL_BESSJ(Order, Z [, /DOUBLE] [, SEQUENCE=value])

## Return Value

The desired value of the modified 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 (optional)

If present and nonzero, then 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).

## Version History

 6.4 Introduced