Goodman's conjecture

Goodman's conjecture on the coefficients of multivalued functions was proposed in complex analysis in 1948 by Adolph Winkler Goodman, an American mathematician.

Let

-valent function.

The conjecture claims the following coefficients hold:

{\displaystyle |b_{n}|\leq \sum _{k=1}^{p}{\frac {2k(n+p)!}{(p-k)!(p+k)!(n-p-1)!

, the conjecture is true for functions of the form

∘ ϕ

is a polynomial and

ϕ

is univalent.