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Re: Integrate problem

• To: mathgroup at smc.vnet.net
• Subject: [mg86213] Re: Integrate problem
• From: "David W.Cantrell" <DWCantrell at sigmaxi.net>
• Date: Thu, 6 Mar 2008 02:57:45 -0500 (EST)
• References: <fqlmo4$jdj$1@smc.vnet.net>

"Michael Weyrauch" <michael.weyrauch at gmx.de> wrote:
> Hello,
>
>   evaluating the integral
>
> Integrate[Sin[1/x]*(Exp[(-a)*x^2]/x), {x, 0, Infinity}, x,
> Assumptions -> a > 0]
>
> in Mathematica 6.0.1 produces
> (1/2)*Pi*HypergeometricPFQ[{}, {1/2, 1}, a/4] -
> Sqrt[a]*Sqrt[Pi]*HypergeometricPFQ[{}, {3/2, 3/2}, a/4]
>
> What is the meaning of the empty list in the first parameter of
> HypergeometricPFQ?

I fail to see how this is an "Integrate problem". But anyway, to answer
your question, it simply means that there are no numeratorial parameters,
and that means that the numerators in the standard series expansion would
all simply be the empty product, and hence, 1.

AFAIK, the two HypergeometricPFQ functions you mentioned do not simplify to
anything more familiar, but many do, for example:

In[5]:= HypergeometricPFQ[{}, {1/2}, a^2/4]

Out[5]= Cosh[a]

David