NAG C Library Function Document

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: $x$ – doubleInput: On entry: the argument $x$ of the function.

Constraint: $|x| \leq \frac{1}{ε^{2}}$ where $ε$ is the machine precision as returned by nag_machine_precision (X02AJC).
2: $fail$ – NagError *Input/Output: The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation 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 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
NE_REAL: 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

nag_struve_h1 (s17gbc) is not threaded in any implementation.

9

Further Comments

For

|x| > \frac{1}{ε^{2}}

H_{1} (x)

is asymptotically close to the Bessel function

Y_{1} (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.

NAG C Library Function Document

nag_struve_h1 (s17gbc)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

1

Purpose

2

Specification

3

Description