nag_complex_bessel_j_seq (s18gkc) (PDF version)
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NAG C Library Manual

NAG Library Function Document

nag_complex_bessel_j_seq (s18gkc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_complex_bessel_j_seq (s18gkc) returns a sequence of values for the Bessel functions Jα+n-1z or Jα-n+1z for complex z, non-negative α<1 and n=1,2,,N+1.

2  Specification

#include <nag.h>
#include <nags.h>
void  nag_complex_bessel_j_seq (Complex z, double a, Integer nl, Complex b[], NagError *fail)

3  Description

nag_complex_bessel_j_seq (s18gkc) evaluates a sequence of values for the Bessel function of the first kind Jαz, where z is complex and nonzero and α is the order with 0α<1. The N+1-member sequence is generated for orders α,α+1,,α+N when N0. Note that + is replaced by - when N<0. For positive orders the function may also be called with z=0, since Jq0=0 when q>0. For negative orders the formula
is used to generate the required sequence. The appropriate values of Jqz and Yqz are obtained by calls to nag_complex_bessel_y (s17dcc) and nag_complex_bessel_j (s17dec).

4  References

Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications

5  Arguments

1:     zComplexInput
On entry: the argument z of the function.
Constraint: z0.0,0.0 when nl<0.
2:     adoubleInput
On entry: the order α of the first member in the required sequence of function values.
Constraint: 0.0a<1.0.
3:     nlIntegerInput
On entry: the value of N.
Constraint: absnl101.
4:     b[absnl+1]ComplexOutput
On exit: with fail.code= NE_NOERROR or NW_SOME_PRECISION_LOSS, the required sequence of function values: b[n-1] contains J α+n-1 z  if nl0 and J α-n+1 z  otherwise, for n=1,2,,absnl+1.
5:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

On entry, argument value had an illegal value.
On entry, absnl=value.
Constraint: absnl101.
On entry, nl=value.
Constraint: when nl<0, z0.0,0.0.
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
Computation abandoned due to the likelihood of overflow.
On entry, a=value.
Constraint: a<1.0.
On entry, a=value.
Constraint: a0.0.
Computation abandoned due to failure to satisfy the termination condition.
Computation abandoned due to total loss of precision.
Computation completed but some precision has been lost.

7  Accuracy

All constants in nag_complex_bessel_y (s17dcc) and nag_complex_bessel_j (s17dec) are specified to approximately 18 digits of precision. If t denotes the number of digits of precision in the floating point arithmetic being used, then clearly the maximum number of correct digits in the results obtained is limited by p=mint,18. Because of errors in argument reduction when computing elementary functions inside nag_complex_bessel_y (s17dcc) and nag_complex_bessel_j (s17dec), the actual number of correct digits is limited, in general, by p-s, where s max1,log10z,log10α  represents the number of digits lost due to the argument reduction. Thus the larger the values of z and α, the less the precision in the result.

8  Further Comments


9  Example

This example evaluates J0z,J1z,J2z and J3z at z=0.6-0.8i, and prints the results.

9.1  Program Text

Program Text (s18gkce.c)

9.2  Program Data

Program Data (s18gkce.d)

9.3  Program Results

Program Results (s18gkce.r)

nag_complex_bessel_j_seq (s18gkc) (PDF version)
s Chapter Contents
s Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012