       Struve functions

• To: mathgroup at smc.vnet.net
• Subject: [mg75646] Struve functions
• From: dimitris <dimmechan at yahoo.com>
• Date: Mon, 7 May 2007 05:40:36 -0400 (EDT)

```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

```

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