NAG CL Interface
s17gac (struve_​h0)

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1 Purpose

s17gac returns the value of the Struve function of order 0, H0(x).

2 Specification

#include <nag.h>
double  s17gac (double x, NagError *fail)
The function may be called by the names: s17gac, nag_specfun_struve_h0 or nag_struve_h0.

3 Description

s17gac 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 function 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 double Input
On entry: the argument x of the function.
Constraint: |x| 1 ε 2 where ε is the machine precision as returned by X02AJC.
2: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
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 7.5 in the Introduction to the NAG Library CL 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 CL Interface for further information.
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 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

Background information to multithreading can be found in the Multithreading documentation.
s17gac 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 (s17gace.c)

10.2 Program Data

Program Data (s17gace.d)

10.3 Program Results

Program Results (s17gace.r)
GnuplotProduced by GNUPLOT 5.4 patchlevel 6 −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 "s17gafe.r" Example Program Returns values for the Struve Function H0(x)