  The theory of Mellin transform is an incredibly useful tool in evaluating
some of the well known results for the zeta function. Ramanujan in his
quarterly reports \cite{1} gave a theorem for Mellin transform which is now
known as Ramanujan's master theorem \cite{2}. In this paper, we have derived
some extended versions of Ramanujan's master theorem based on our previous
results \cite{3} and applied them to some special functions such as known as
the Riesz function $R(z)$ and generalized binomial function. Some asymptotic
expansions using extended Ramanujan's master theorem are also derived.
