New explicit formulas for the coefficients of $p$-symmetric functions

Abstract:

In comparison with Goodman’s well-known method and results, we use an alternate method by which we obtain more tractable formulas for the coefficients of p-symmetric univalent functions of classes ${S^p}$ and ${\Sigma ^p}$ in terms of the coefficients of their associated functions in the class s. Our method and results are simple and convenient and they make it easier to compute the coefficients for functions in the classes ${S^p}$ and ${\Sigma ^p}$, because we obtain a new recursion formula for them.