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
J-qz=cosπqJqz-sinπqYqz
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

NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, absnl=value.
Constraint: absnl101.
On entry, nl=value.
Constraint: when nl<0, z0.0,0.0.
NE_INTERNAL_ERROR
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.
NE_OVERFLOW_LIKELY
Computation abandoned due to the likelihood of overflow.
NE_REAL
On entry, a=value.
Constraint: a<1.0.
On entry, a=value.
Constraint: a0.0.
NE_TERMINATION_FAILURE
Computation abandoned due to failure to satisfy the termination condition.
NE_TOTAL_PRECISION_LOSS
Computation abandoned due to total loss of precision.
NW_SOME_PRECISION_LOSS
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

None.

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