NAG FL Interface
s17gaf (struve_​h0)

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1 Purpose

s17gaf returns the value of the Struve function of order 0, H0(x), via the function name.

2 Specification

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

3 Description

s17gaf evaluates an approximation to the Struve function of order zero, H0(x).
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

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

5 Arguments

1: x Real (Kind=nag_wp) Input
On entry: the argument x of the function.
Constraint: |x| 1 ε 2 where ε is the machine precision as returned by x02ajf.
2: 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 -1 or 1 is used it is essential to test the value of ifail on exit.
On exit: ifail=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry 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:
x is too large and the routine returns zero.
An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
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.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface 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 floating-point arithmetic being used t, then clearly the maximum number of correct digits in the results obtained is limited by p=min(t,20).
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

s17gaf is not threaded in any implementation.

9 Further Comments

For |x| > 1 ε 2 , H0(x) is asymptotically close to the Bessel function Y0(x) 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 (s17gafe.f90)

10.2 Program Data

Program Data (s17gafe.d)

10.3 Program Results

Program Results (s17gafe.r)
GnuplotProduced by GNUPLOT 5.0 patchlevel 3 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 −10 −8 −6 −4 −2 0 2 4 6 8 10 H0(x) x Example Program Returns values for the Struve Function H0(x) "s17gafe.r"