       Re: StruveH runtime error

• To: mathgroup at smc.vnet.net
• Subject: [mg45680] Re: StruveH runtime error
• From: vb at cybertester.com (Vladimir Bondarenko)
• Date: Mon, 19 Jan 2004 05:15:23 -0500 (EST)
• References: <buap11\$mim\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```"Toshiyuki \(Toshi\) Meshii" <meshii at mech.fukui-u.ac.jp> wrote in message news:<buap11\$mim\$1 at smc.vnet.net>...

TM> StruveH[1,10^5]

TM> Microsoft Visual C++ Runtime Library Runtime Error!
TM> Program......\Mathkernel.exe
TM> abnormal program termination.

TM> Can someone help me on calculating StruveH functions
TM> for large values by Mathematica?

I confirm that you re-discovered a bug in Mathematica 5 I
reported to Stephen Wolfram on 1 Sep 2001 22:26:38 in the
CHAPTER 1: Integration: Simplest Elementary Functions of
my memoir OPPORTUNITIES TO IMPROVE THE MATHKERNEL under
# 385 and # 467. For example, the entry # 467 refers to

NProduct[StruveH[0, n], {n, 1, Infinity}]

In Mathematica 5.0, this expression invokes

Runtime Error: Microsoft Visual C++ Runtime Library

I have already sent you report to support at wolfram.com .

The solution to your problem is to use asymptotic expansions:

StruveH[1,z] -> (2-Sqrt[Pi/z](Cos[z]+Sin[z]))/Pi + O(1/z^(3/2))

In := \$Version

Out = 5.0 for Microsoft Windows (June 11, 2003)

In := (2 - Sqrt[Pi/z](Cos[z]+Sin[z]))/Pi/.z -> 10^4//N//Timing

Out = {0. Second, 0.643716}

In:= (2-Sqrt[Pi/z](Cos[z]+Sin[z]))/Pi/.z->10^5//N//Timing

Out= {0. Second, 0.638339}

In:= (2-Sqrt[Pi/z](Cos[z]+Sin[z]))/Pi /.z ->10^1000000//N//Timing

Out= {0.831 Second, 0.63662}

By the way, StruveH[1,z] satisfies the following ODE

In:= DSolve[{z^2y''[z] + z y'[z] + (z^2 - 1)y[z] == 2/P z^2,\
y == 0, y' == 0}, y[z], z]

(* unfortunately, Mathematica 5 fails here *)

Out= {}   (* expected:  StruveH[1, z] *)

which is yet another bug.

Best wishes,

GEMM architect
Co-founder, CEO, Mathematical Director
Cyber Tester, LLC

http://www.cybertester.com/
http://www.CAS-testing.org/

................................................................

```

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