NAG CL Interfaces17gbc (struve_​h1)

1Purpose

s17gbc returns the value of the Struve function of order $1$, ${H}_{1}\left(x\right)$.

2Specification

 #include
 double s17gbc (double x, NagError *fail)
The function may be called by the names: s17gbc, nag_specfun_struve_h1 or nag_struve_h1.

3Description

s17gbc 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 function 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: $\mathbf{x}$double 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 X02AJC.
2: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_INTERNAL_ERROR
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.
NE_NO_LICENCE
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.
NE_REAL
x is too large and the function returns zero.

7Accuracy

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 $p=\mathrm{min}\phantom{\rule{0.125em}{0ex}}\left(t,20\right)$.
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

s17gbc 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.

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 (s17gbce.c)

10.2Program Data

Program Data (s17gbce.d)

10.3Program Results

Program Results (s17gbce.r)