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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[1] := $Version
Out[1] = 5.0 for Microsoft Windows (June 11, 2003)
In[2] := (2 - Sqrt[Pi/z](Cos[z]+Sin[z]))/Pi/.z -> 10^4//N//Timing
Out[2] = {0. Second, 0.643716}
In[3]:= (2-Sqrt[Pi/z](Cos[z]+Sin[z]))/Pi/.z->10^5//N//Timing
Out[3]= {0. Second, 0.638339}
In[4]:= (2-Sqrt[Pi/z](Cos[z]+Sin[z]))/Pi /.z ->10^1000000//N//Timing
Out[4]= {0.831 Second, 0.63662}
By the way, StruveH[1,z] satisfies the following ODE
In[5]:= DSolve[{z^2y''[z] + z y'[z] + (z^2 - 1)y[z] == 2/P z^2,\
y[0] == 0, y'[0] == 0}, y[z], z]
(* unfortunately, Mathematica 5 fails here *)
Out[5]= {} (* expected: StruveH[1, z] *)
which is yet another bug.
Best wishes,
Vladimir Bondarenko
GEMM architect
Co-founder, CEO, Mathematical Director
Cyber Tester, LLC
http://www.cybertester.com/
http://www.CAS-testing.org/
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