Some results on the asymptotic behaviour of coefficients of large powers of functions (Q1893987)

The author presents extensions of reviewed results of the asymptotic approximation of the coefficient of order \(n\) of a function \(f(z)^d\) when \(n\) and \(d\) grow large while staying roughly proportional allowing more general relationships between \(n\) and \(d\) and taking into account a multiplicative factor \(\psi (z)\). A common feature of all these results is the use of a saddle point approximation (in particular simpler results can be given).