Chapter 16: Mellin–Barnes integrals and Mellin convolution integrals

Abstract:

In §2.5 we have given examples in which the idea of Watson's lemma can be used for integrals of the form

This integral reduces to the standard form of Watson's lemma when the kernel h(t) = e^-t. For different kernels we have explained how the method can be modified. We have observed that in some cases the moments may not exist for all n. By using certain analytic properties of special kernels, such as J_ν(t), it is still possible to obtain an asymptotic expansion. However, a more systematic approach will be welcome…