# NAG FL Interfaces17gaf (struve_​h0)

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## 1Purpose

s17gaf returns the value of the Struve function of order $0$, ${H}_{0}\left(x\right)$, via the function name.

## 2Specification

Fortran Interface
 Function s17gaf ( x,
 Real (Kind=nag_wp) :: s17gaf Integer, Intent (Inout) :: ifail Real (Kind=nag_wp), Intent (In) :: x
#include <nag.h>
 double s17gaf_ (const double *x, Integer *ifail)
The routine may be called by the names s17gaf or nagf_specfun_struve_h0.

## 3Description

s17gaf evaluates an approximation to the Struve function of order zero, ${H}_{0}\left(x\right)$.
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.

## 4References

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

s17gaf is not threaded in any implementation.

For $|{\mathbf{x}}|>\frac{1}{{\epsilon }^{2}}$, ${H}_{0}\left(x\right)$ is asymptotically close to the Bessel function ${Y}_{0}\left(x\right)$ 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 (s17gafe.f90)

### 10.2Program Data

Program Data (s17gafe.d)

### 10.3Program Results

Program Results (s17gafe.r)