Asymptotic expansions and positivity of coefficients for large powers of analytic functions (Q1864340)

Asymptotic expansions are derived of coefficients of \((f(z))^n\), where \(f\) is an entire analytic function satisfying \(| f(z)| <f(| z| )\) for complex \(z\) off the positive real line. Conditions on \(f\) are given such that \((f(z))^n\) has only positive coefficients, if \(n\) is large enough.