Generalised Euler-Jacobi Inversion Formula and Asymptotics beyond All Orders

This work, first published in 1995, presents developments in understanding the subdominant exponential terms of asymptotic expansions which have previously been neglected. By considering special exponential series arising in number theory, the authors derive the generalised Euler-Jacobi series, expressed in terms of hypergeometric series. Dingle''s theory of terminants is then employed to show how...