Asymptotic approximations for Generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi Polynomials in terms of Hyperbolic Functions

Abstract

Asymptotic approximation formulas for polynomials of the type Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi with integer order and real parameters are obtained via hyperbolic functions. The derivation of the formulas is done using the principle of saddle point and expansion of appropriate hyperbolic function about a saddle point.