       Re: Struve functions

• To: mathgroup at smc.vnet.net
• Subject: [mg75674] Re: [mg75626] Struve functions
• From: DrMajorBob <drmajorbob at bigfoot.com>
• Date: Tue, 8 May 2007 05:56:02 -0400 (EDT)
• Organization: Deep Space Corps of Engineers
• References: <28975181.1178533667715.JavaMail.root@m35>

```Version 6 can do this:

strs = HoldForm[Integrate[{StruveH[n, x], StruveL[n, x]}, x]];
ReleaseHold@strs

{2^(-2 - n)*x^(2 + n)*Gamma[1 + n/2]*HypergeometricPFQRegularized[{1, 1 =
=

+ n/2}, {3/2 + n, 3/2, 2 + n/2}, -(x^2/4)],2^(-2 - n)*x^(2 + n)*Gamma[1 =
=

+ n/2]*HypergeometricPFQRegularized[{1, 1 + n/2}, {3/2 + n, 3/2, 2 + n/2=
},  =

x^2/4]}

Bobby

On Mon, 07 May 2007 04:29:52 -0500, dimitris <dimmechan at yahoo.com> wrote=
:

> Hello.
>
> \$VersionNumber
> 5.2
>
> Consider the indefinite integral of the functions StruveH[n, x] and
> StruveL[n, x]
>
> strs = HoldForm[Integrate[{StruveH[n, x], StruveL[n, x]}, x]]
>
> ReleaseHold@strs
> {Integrate[StruveH[n, x], x], Integrate[StruveL[n, x], x]}
>
> It seems that Mathematica can't get the antiderivative of these
> functions.
>
> However,
>
> strs /. Integrate[f_, o_] :> Integrate[f, {o, 0, t}, Assumptions -> n
>> -2]//
>           ReleaseHold//FunctionExpand
> {(t^(2 + n)*HypergeometricPFQ[{1, 1 + n/2}, {3/2, 2 + n/2, 3/2 + n}, -=

> (t^2/4)])/(2^n*((2 + n)*Sqrt[Pi]*Gamma[3/2 + n])), (t^(2 +
> n)*HypergeometricPFQ[{1, 1 + n/2}, {3/2, 2 + n/2, 3/2 + n}, t^2/4])/
> (2^n*((2 + n)*Sqrt[Pi]*Gamma[3/2 + n]))}
>
> which are indeed antiderivatives of the functions
>
> FunctionExpand[D[ints, t]]
> {StruveH[n, t], StruveL[n, t]}
>
> Am I the only one that see an incosistency here or not?
> How is it possible, since Mathematica failes to get the indefinite
> integrals,
> to evaluate the definite ones (of course I am aware of the table look-=

> up possibility
> and the Marichev-Adamchik Mellin transform methods but I think here is=

> not the case).
>
> Any insight/explanations?
>
> Dimitris
>
>
>

-- =

DrMajorBob at bigfoot.com

```

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