# Invert a transcendental function

I have tried Reduce and Solve in Mathematica, as well as have a long list of tries in Maple, but cannot seem to get anywhere solving the following for V:

V^P * (V-1)^Q == c^(P-Q) * X^Q * (V-c^2)^Q,


where P,Q are positive integers; V>0; U>0 and X = U^Q * V^P; c = Exp[t/2] where t is i times a real number.

Any suggestions would be great.

Btw, I can share a Maple file (http://ubuntuone.com/5WGrFF8PYXR8LSwNB95SRW) where I tried a Fixed-Point/Contraction attempt, a series inverse attempt, and even the Lagrangian Inversion method. For the most part I seem to run out of computing power when I try to get to decent orders of approximation...

P.S. I am looking for a symbolic solution, at least to a few orders.

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Are you looking for a symbolic or numerical solution? – Szabolcs Feb 13 '14 at 21:51
So you are looking a symbolic approximation for V in terms of U while the rest (P,Q,c) are parameters? – Szabolcs Feb 13 '14 at 21:55
Well eventually I need V(X), either as a polynomial... and yes, P, Q, and c are parameters. – nate Feb 13 '14 at 21:58
Here's a way to invert just about any equation: Rotate[V^P*(V - 1)^Q == c^(P - Q)*X^Q*(V - c^2)^Q, Pi] – bill s Feb 13 '14 at 23:25
@bills, you're missing a HoldForm :) – RunnyKine Feb 14 '14 at 3:13