Solutions to a Problem in Power Series Reversion

This paper presents the general solution of the following problem in two forms. Let $f(x,y)$ be defined by the formal power series $f(x,y) = \sum _{m = 0}^\infty \sum _{n = 0}^\infty f_{mn} x^m y^n $ with $f_{00} \ne 0$. If v satisfies $v(x,y) = f(xv^a ,yv^b )$, where a and b are constants, then find the formal power series expansion of $v^c(x,y)$, where c is also a constant. A special case.of this problem, which occurs in a paper by R. A. Handelsman and J. S. Lew [1], has been proposed as a problem to be solved by computer using a symbolic algebra system [2].