# NAG FL Interfaces17gbf (struve_​h1)

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## 1Purpose

s17gbf returns the value of the Struve function of order $1$, ${H}_{1}\left(x\right)$, via the function name.

## 2Specification

Fortran Interface
 Function s17gbf ( x,
 Real (Kind=nag_wp) :: s17gbf Integer, Intent (Inout) :: ifail Real (Kind=nag_wp), Intent (In) :: x
#include <nag.h>
 double s17gbf_ (const double *x, Integer *ifail)
The routine may be called by the names s17gbf or nagf_specfun_struve_h1.

## 3Description

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.
NIST Digital Library of Mathematical Functions
MacLeod A J (1996) MISCFUN, a software package to compute uncommon special functions ACM Trans. Math. Software (TOMS) 22(3) 288–301

## 5Arguments

1: $\mathbf{x}$Real (Kind=nag_wp) Input
On entry: the argument $x$ of the function.
Constraint: $|{\mathbf{x}}|\le \frac{1}{{\epsilon }^{2}}$ where $\epsilon$ is the machine precision as returned by x02ajf.
2: $\mathbf{ifail}$Integer Input/Output
On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.
If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ 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).

## 6Error 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.
${\mathbf{ifail}}=-99$
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

## 7Accuracy

The Chebyshev coefficients used by this routine are internally represented to $20$ digits of precision. Calling the number of digits of precision in the floating-point 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.

## 8Parallelism and Performance

s17gbf is not threaded in any implementation.

For $|{\mathbf{x}}|>\frac{1}{{\epsilon }^{2}}$, ${H}_{1}\left(x\right)$ is asymptotically close to the Bessel function ${Y}_{1}\left(x\right)$ which is approximately zero to machine precision.

## 10Example

This example reads values of the argument $x$ from a file, evaluates the function at each value of $x$ and prints the results.

### 10.1Program Text

Program Text (s17gbfe.f90)

### 10.2Program Data

Program Data (s17gbfe.d)

### 10.3Program Results

Program Results (s17gbfe.r)