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>
- Reply-to: drmajorbob at bigfoot.com
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