NAG C Library Function Document
nag_struve_h1 (s17gbc)
1
Purpose
nag_struve_h1 (s17gbc) returns the value of the Struve function of order $1$, ${H}_{1}\left(x\right)$.
2
Specification
#include <nag.h> 
#include <nags.h> 
double 
nag_struve_h1 (double x,
NagError *fail) 

3
Description
nag_struve_h1 (s17gbc) evaluates an approximation to the Struve function of order $1$, ${H}_{1}\left(x\right)$.
Please consult the
NIST Digital Library of Mathematical Functions for a detailed discussion of the Struve function including special cases, transformations, relations and asymptotic approximations.
The approximation method used by this function is based on Chebyshev expansions.
4
References
MacLeod A J (1996) MISCFUN, a software package to compute uncommon special functions ACM Trans. Math. Software (TOMS) 22(3) 288–301
5
Arguments
 1:
$\mathbf{x}$ – doubleInput

On entry: the argument $x$ of the function.
Constraint:
$\left{\mathbf{x}}\right\le \frac{1}{{\epsilon}^{2}}$ where
$\epsilon $ is the
machine precision as returned by
nag_machine_precision (X02AJC).
 2:
$\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see
Section 3.7 in How to Use the NAG Library and its Documentation).
6
Error Indicators and Warnings
 NE_ALLOC_FAIL

Dynamic memory allocation failed.
See
Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
 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.
See
Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
 NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See
Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
 NE_REAL

x is too large and the function returns zero.
7
Accuracy
The Chebyshev coefficients used by this function are internally represented to $20$ digits of precision. Calling the number of digits of precision in the floatingpoint arithmetic being used $t$, then clearly the maximum number of correct digits in the results obtained is limited by $p=\mathrm{min}\phantom{\rule{0.125em}{0ex}}\left(t,20\right)$.
Apart from this, rounding errors in internal arithmetic may result in a slight loss of accuracy, but it is reasonable to assume that the result is accurate to within a small multiple of the machine precision.
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Parallelism and Performance
nag_struve_h1 (s17gbc) is not threaded in any implementation.
For $\left{\mathbf{x}}\right>\frac{1}{{\epsilon}^{2}}$, ${H}_{1}\left(x\right)$ is asymptotically close to the Bessel function ${Y}_{1}\left(x\right)$ which is approximately zero to machine precision.
10
Example
This example reads values of the argument $x$ from a file, evaluates the function at each value of $x$ and prints the results.
10.1
Program Text
Program Text (s17gbce.c)
10.2
Program Data
Program Data (s17gbce.d)
10.3
Program Results
Program Results (s17gbce.r)