Re: Calculating a simple integral
- To: mathgroup at smc.vnet.net
- Subject: [mg131098] Re: Calculating a simple integral
- From: "Brambilla Roberto Luigi (RSE)" <Roberto.Brambilla at rse-web.it>
- Date: Tue, 11 Jun 2013 02:31:31 -0400 (EDT)
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I have for semplicity rewritten your integral as f[x_,a_]:= Sqrt[2]Sin[x/2]/(x(x^2+a^2)(x+2Pi)(x-2Pi)) (*this function is NOT singular in 0,2Pi,-2Pi*) The numerical integration is readily obtained kr=0.09; int1=2 NIntegrate[f[kz,kr]^2,{kz,0,Infinity}] (*the integrand is even*) 0.691084 Also the indefinite integral is obtained in a couple of minutes (ver.8) int2=Integrate[f[kz,kr]^2,{kz,0,Infinity}]=.... The result is a long expression that can be rewritten as foo1[x_,y_]:=Im[MejerG[{{1,1,3/2},{}},{{1,1,3/2},{0,1/2}},x,y]] foo2[x_,y_]:=Im[MejerG[{{1,1,3/2},{}},{{1,3/2,2},{0,1/2}},x,y]] A=3 kr^7+28 kr^5 Pi2+ +16 Pi^5/2(5 kr^2+4Pi^2)*foo1[I kr/2,1/2]+ +32Pi^5/2(kr^2+4Pi^2)*foo2[I kr/2,1/2] 249.281 B=32 kr^5 Pi^3 (kr^2+4PI^2) 360.71 int2=A/B 0.691084 Bye Roberto RSE SpA ha adottato il Modello Organizzativo ai sensi del D.Lgs.231/2001, inforza del quale l'assunzione di obbligazioni da parte della Societ=E0 avviene con firma di un procuratore, munito di idonei poteri. RSE adopts a Compliance Programme under the Italian Law (D.Lgs.231/2001). According to this RSE Compliance Programme, any commitment of RSE is taken by the signature of one Representative granted by a proper Power of Attorney. Le informazioni contenute in questo messaggio di posta elettronica sono riservate e confidenziali e ne e' vietata la diffusione in qualsiasi modo o forma. Qualora Lei non fosse la persona destinataria del presente messaggio, Lainvitiamo a non diffonderlo e ad eliminarlo, dandone gentilmente comunicazione al mittente. The information included in this e-mail and any attachments are confidential and may also be privileged. If you are not the correct recipient, you are kindly requested to notify the sender immediately, to cancel it and not to disclose the contents to any other person.