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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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