Re: Bug in StruveH

• To: mathgroup at yoda.ncsa.uiuc.edu
• Subject: Re: Bug in StruveH
• From: Steve Christensen <stevec at yoda.ncsa.uiuc.edu>
• Date: Sun, 10 Feb 91 18:07:20 +0100

```pjanhune at finsun.csc.fi writes:

> The package StruveH.m from the book by Roman Maeder contains the
> following bug:
>
> When called with an integer or rational second argument, the function
> StruveH returns an exact-looking result, which is WRONG!! It's only
> the first term of the series expansion. For floating-point arguments
> or complex numbers the function behaves correctly. One cure is to insert
> the line
> ....

There is indeed a bug in the numerical code of Struve[].
It should not be called with an exact second argument.
Therefore the rule should be made conditional as follows:

(* numerical evaluation *)

StruveH[nu_?NumberQ, z_?NumberQ] :=
Block[{s=0, so=-1, m=0, prec = Precision[z],
z2 = -(z/2)^2,k1 = 3/2, k2 = nu + 3/2, g1, g2, zf},
zf = (z/2)^(nu+1); g1 = Gamma[k1]; g2 = Gamma[k2];
While[so != s,
so = s; s += N[zf/g1/g2, prec];
g1 *= k1; g2 *= k2; zf *= z2;
k1++; k2++; m++
];
s
] /; Precision[z] < Infinity

(The proposed fix by pjanhune at finsun.csc.fi has the disadvantage
of giving an inexact result for exact input. This is contrary to
Mathematica's philosophy. One should use N[StruveH[...]] for this.)

This has already been fixed for the second edition of my book.
All the packages from the book will be part of Mathematica 2.0.

Roman Maeder

```

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