Abstract
Hardy's class of functions for the Ramanujan interpolation formula and Ramanujan-Hardy master theorem is extended to a wider domain of applicability and the extension is illustrated by examples.MSC: 11M06, 11M26, 11M36, 11M99, 42 A32, 11M06, 42A32
Highlights
Ramanujan was in a class by himself as an intuitive mathematician and provided many results that have kept generations of mathematicians busy to prove them rigorously
For the interpolation formula, which is used in proving the master theorem, Hardy proved it using the domain (0, π) for the parameter A that appeared in the proof
We introduce the notation for the Weyl transform of a function that is found helpful in stating the master theorem and other related results precisely
Summary
Ramanujan was in a class by himself as an intuitive mathematician and provided many results that have kept generations of mathematicians busy to prove them rigorously (see [1,2]). We give applications of the master theorem by introducing a larger class of functions using Mellin and Weyl transforms. We introduce the notation for the Weyl transform of a function that is found helpful in stating the master theorem and other related results precisely.
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