Mellin transform methods applied to integral evaluation: Taylor series and asymptotic approximations

Mellin transform methods have been used to obtain Taylor series or asymptotic approximations to definite integrals whose integrands consist of the product of two generalized hypergeometric functions. This approach has proved extremely useful in many applied physics problems including the analysis of electromagnetic propagation in a turbulent medium. The main result in this article is a generalization of the method to integrands containing the product of an arbitrary number of hypergeometric functions providing a very powerful and general technique for integral evaluation with many applications in physics.