Re: Help to solve an integral by using Mathematica Integrate[Sqrt[t

*To*: mathgroup at smc.vnet.net*Subject*: [mg112852] Re: Help to solve an integral by using Mathematica Integrate[Sqrt[t*From*: Valeri Astanoff <astanoff at gmail.com>*Date*: Sun, 3 Oct 2010 05:41:08 -0400 (EDT)*References*: <i84adn$gvn$1@smc.vnet.net> <i84bkk$hqk$1@smc.vnet.net> <i86v14$hqv$1@smc.vnet.net>

On 2 oct, 11:46, Hugo <hpe650... at gmail.com> wrote: > Valeri, > > Suggested solution is very close to solution found in book. How did > you get it? Please, let me know how did you implement this integral. > Good day, Leonid's solution : Re[-(2/15) I (2 (1 + (-1 + z) z) EllipticE[1 - z] - 2 (1 + (-1 + z) z) EllipticE[I ArcCoth[Sqrt[z]], 1 - z] + z (1 + z) (EllipticF[I ArcCoth[Sqrt[z]], 1 - z] - EllipticK[1 - z]))]; and my own : (1/15)*(4*(1 + (z-1)*z)*EllipticE[z] - 2*(2 + (z-3)*z)*EllipticK[z]) are numerically identical when z lies between 0 and 1. I observed that for most rational values of z, the solution was a linear combination of EllipticE and EllipticK. Then I performed a polynomial fitting of the coefficients. Well, I confess I sort of guessed it... -- Valeri