Elliptic integral
- To: mathgroup at smc.vnet.net
- Subject: [mg67679] Elliptic integral
- From: Ian Linington <i.e.linington at sussex.ac.uk>
- Date: Tue, 4 Jul 2006 01:58:03 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Hello, does anybody know of a Mathematica program which converts an
elliptic integral of the form int z^n/sqrt(P(z)) dz, where P is a
fourth-order polynomial, into one of the standard forms?
The reason that I would like this is to try and evaluate
Integrate[
Exp[q*I*x]/(Sqrt(-A*Exp[4*I*x] - I*B*Exp[3*I*x] + (C+I*D)*Exp[2*I*x]
+ I*B*Exp[I*x] - A)), {x, 0, 2*Pi},
Assumptions -> {Element[q, Integers], A > 0, B > 0, C > 0, D > 0]
but Mathematica won't do it in one go, even if I choose specific values
for A, B, C, D and q. I believe that an analytic solution does exist,
but to decompose the integral in terms of Jacobi ellpitic functions
looks like a painful process.
Any help would be greatly appreciated!
Thanks,
Ian