NAG Library Routine Document
s17gbf (struve_h1)
1
Purpose
s17gbf returns the value of the Struve function of order $1$, ${H}_{1}\left(x\right)$, via the function name.
2
Specification
Fortran Interface
Real (Kind=nag_wp)  ::  s17gbf  Integer, Intent (Inout)  ::  ifail  Real (Kind=nag_wp), Intent (In)  ::  x 

C Header Interface
#include <nagmk26.h>
double 
s17gbf_ (const double *x, Integer *ifail) 

3
Description
s17gbf 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 routine 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: $\mathbf{x}$ – Real (Kind=nag_wp)Input

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
x02ajf.
 2: $\mathbf{ifail}$ – IntegerInput/Output

On entry:
ifail must be set to
$0$,
$1\text{or}1$. If you are unfamiliar with this argument you should refer to
Section 3.4 in How to Use the NAG Library and its Documentation for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value
$1\text{or}1$ is recommended. If the output of error messages is undesirable, then the value
$1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is
$0$.
When the value $\mathbf{1}\text{or}\mathbf{1}$ is used it is essential to test the value of ifail on exit.
On exit:
${\mathbf{ifail}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see
Section 6).
6
Error Indicators and Warnings
If on entry
${\mathbf{ifail}}=0$ or
$1$, explanatory error messages are output on the current error message unit (as defined by
x04aaf).
Errors or warnings detected by the routine:
 ${\mathbf{ifail}}=1$

x is too large and the routine returns zero.
 ${\mathbf{ifail}}=99$
An unexpected error has been triggered by this routine. Please
contact
NAG.
See
Section 3.9 in How to Use the NAG Library and its Documentation for further information.
 ${\mathbf{ifail}}=399$
Your licence key may have expired or may not have been installed correctly.
See
Section 3.8 in How to Use the NAG Library and its Documentation for further information.
 ${\mathbf{ifail}}=999$
Dynamic memory allocation failed.
See
Section 3.7 in How to Use the NAG Library and its Documentation for further information.
7
Accuracy
The Chebyshev coefficients used by this routine 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.
8
Parallelism and Performance
s17gbf 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 (s17gbfe.f90)
10.2
Program Data
Program Data (s17gbfe.d)
10.3
Program Results
Program Results (s17gbfe.r)