Re: Integrate problem

• To: mathgroup at smc.vnet.net
• Subject: [mg86204] Re: [mg86185] Integrate problem
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Thu, 6 Mar 2008 02:56:03 -0500 (EST)
• Reply-to: hanlonr at cox.net

```Look at the TraditionalForm and you will see that HypergeometricPFQ[{}, {b1, b2}, z] is 0F2[{}, {b1, b2}, z], i.e., there are no numerator parameters in the series expansion

SeriesCoefficient[HypergeometricPFQ[{}, {b1, b2}, z], {z, 0, n}] ==
1/(Pochhammer[b1, n]*Pochhammer[b2, n]*n!) // FullSimplify

True

Bob Hanlon

---- Michael Weyrauch <michael.weyrauch at gmx.de> wrote:
> Hello,
>
>   evaluating the integral
>
> Integrate[Sin[1/x]*(Exp[(-a)*x^2]/x), {x, 0, Infinity}, 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?
>
> Thanks for answers,
>
> Michael Weyrauch
>
>

```

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