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NAG Toolbox: nag_specfun_bessel_j_seq_complex (s18gk)


    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example


nag_specfun_bessel_j_seq_complex (s18gk) 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.


[b, ifail] = s18gk(z, a, nl)
[b, ifail] = nag_specfun_bessel_j_seq_complex(z, a, nl)


nag_specfun_bessel_j_seq_complex (s18gk) 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_specfun_bessel_y_complex (s17dc) and nag_specfun_bessel_j_complex (s17de).


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


Compulsory Input Parameters

1:     z – complex scalar
The argument z of the function.
Constraint: z0.0,0.0 when nl<0.
2:     a – double scalar
The order α of the first member in the required sequence of function values.
Constraint: 0.0a<1.0.
3:     nl int64int32nag_int scalar
The value of N.
Constraint: absnl101.

Optional Input Parameters


Output Parameters

1:     babsnl+1 – complex array
With ifail=0 or 3, the required sequence of function values: bn contains J α+n-1 z if nl0 and J α-n+1 z otherwise, for n=1,2,,absnl+1.
2:     ifail int64int32nag_int scalar
ifail=0 unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

Cases prefixed with W are classified as warnings and do not generate an error of type NAG:error_n. See nag_issue_warnings.

On entry,z=0.0,0.0 when nl<0,
The computation has been abandoned due to the likelihood of overflow.
W  ifail=3
The computation has been completed but some precision has been lost.
The computation has been abandoned due to total loss of precision.
The computation has been abandoned due to failure to satisfy the termination condition.
An unexpected error has been triggered by this routine. Please contact NAG.
Your licence key may have expired or may not have been installed correctly.
Dynamic memory allocation failed.


All constants in nag_specfun_bessel_y_complex (s17dc) and nag_specfun_bessel_j_complex (s17de) 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_specfun_bessel_y_complex (s17dc) and nag_specfun_bessel_j_complex (s17de), 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.

Further Comments



This example evaluates J0z,J1z,J2z and J3z at z=0.6-0.8i, and prints the results.
function s18gk_example

fprintf('s18gk example results\n\n');

z =  0.6 - 0.8i;
a = 0;
nl = int64(3);

[b, ifail] = s18gk(z, a, nl);

fprintf('   alpha        J_alpha(%5.1f%+5.1fi)\n',real(z), imag(z));
for j=1:nl+1
  fprintf('%10.2e   %12.4e%+12.4ei\n', a+double(j-1), real(b(j)), imag(b(j)));

s18gk example results

   alpha        J_alpha(  0.6 -0.8i)
  0.00e+00     1.0565e+00 +2.4811e-01i
  1.00e+00     3.5825e-01 -3.7539e-01i
  2.00e+00    -2.5974e-02 -1.2538e-01i
  3.00e+00    -1.9369e-02 -8.6380e-03i

PDF version (NAG web site, 64-bit version, 64-bit version)
Chapter Contents
Chapter Introduction
NAG Toolbox

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