# 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.

• Are you looking for a symbolic or numerical solution? Commented Feb 13, 2014 at 21:51
• So you are looking a symbolic approximation for V in terms of U while the rest (P,Q,c) are parameters? Commented Feb 13, 2014 at 21:55
• Well eventually I need V(X), either as a polynomial... and yes, P, Q, and c are parameters.
– nate
Commented Feb 13, 2014 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] Commented Feb 13, 2014 at 23:25
• @bills, you're missing a HoldForm :) Commented Feb 14, 2014 at 3:13