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