Re: Integrate Bug

*To*: mathgroup at smc.vnet.net*Subject*: [mg100593] Re: Integrate Bug*From*: Valeri Astanoff <astanoff at gmail.com>*Date*: Tue, 9 Jun 2009 03:52:47 -0400 (EDT)*References*: <gv2jh5$97b$1@smc.vnet.net> <h0btr4$8ju$1@smc.vnet.net>

On 8 juin, 12:17, Valeri Astanoff <astan... at gmail.com> wrote: > On 5 juin, 22:05, Valeri Astanoff <astan... at gmail.com> wrote: > > > > > > > On 21 mai, 05:58, Ney Lemke <ney.nle... at gmail.com> wrote: > > > > I am trying to calculate this integral that should be positive.But th= e > > > answer is 0. > > > > In: Integrate[(1)/(z^2 + b^2 + a^2 - 2 z b Sin[\[Theta]] - > > > 2 a b Cos[\[Theta]])^(1/2), {\[Theta], 0, 2 \[Pi]}, > > > Assumptions -> {a > 0, b > 0, z > 0}] > > > > Out:0 > > > > Anybody have notice a situation like that? > > > > My platform is MacOSX 10.4 and Mathematica 7. > > > > Best wishes, > > > Further to my previous post, seems that one single formula suffices : > > > F[a_, b_, z_] := > > (4 Sqrt[a^2 + b^2 + z^2 + 2 b Sqrt[a^2 + z^2]]* > > Abs[Im[EllipticK[(a^4 + b^4 + 6 b^2 z^2 + z^4 + > > 4 b^3 Sqrt[a^2 + z^2] + 4 b z^2 Sqrt[a^2 + z^2] + > > 2 a^2 (3 b^2 + z^2 + 2 b Sqrt[a^2 + z^2]))/ > > (a^2 - b^2 + z^2)^2]]])/Abs[a^2 - b^2 + z^2] > > > -- > > V.Astanoff > > 2009/6/6 Andreas Dieckmann <adieck... at aol.com> > > Hi, > > your expression with the complex EllipticK for the integral can be > further simplified to: > > (4/Sqrt[a^2 + b^2 + z^2 + 2*b*Sqrt[a^2 + z^2]]) EllipticK[(4*b* > Sqrt[a^2 + z^2])/(a^2 + b^2 + z^2 + 2*b*Sqrt[a^2 + z^2])] > > Greetings > > Andreas- Masquer le texte des messages pr=E9c=E9dents - > > - Afficher le texte des messages pr=E9c=E9dents - Dear Andreas, Congratulations : you crunched and squeezed my awful formula more then can FullSimplify ! Could you please spare a few moments to explain (for those like me who are not very familiar with EllipticK) the way you did it ? Thanks in advance -- Valeri Astanoff