1 citations · 1 across the 9 of their papers we have counts for
9 papers
Functional equation for Mellin transform of Fourier series associated with modular forms
Omprakash Atale
Let and denote the Mellin transforms of and , respectively. Ramanujan investigated the functions and that satisfy the funct…
On Finite Mellin Transform via Ramanujan's Master Theorem
Omprakash Atale
This paper aims to show that by making use of Ramanujan's Master Theorem and the properties of the lower incomplete gamma function, it is possible to construct a finite Mellin tran…
A Generalized Ramanujan Master Theorem and Integral Representation of Meromorphic Functions
Zachary P. Bradshaw, Omprakash Atale
Ramanujan's Master Theorem is a decades-old theorem in the theory of Mellin transforms which has wide applications in both mathematics and high energy physics. The unconventional m…
Galois connections and isomorphism of simultaneous ordered relations
Omprakash Atale
In order theory, partially ordered sets are only equipped with one relation which decides the entire structure/Hasse diagram of the set. In this paper, we have presented how partia…
On some generalized number theoretic functions and Ighachanea-Akkouchia Holder's inequalities
Omprakash Atale
Recently, it has been shown by Ighachanea and Akkouchia \cite{0.1} that using binomial coefficients, one can derive some new refinements of Holder's inequalities. This inequalities…
Type-(I,II) Interpolations and some asymptotic expansions using Ramanujan's master theorem
Omprakash Atale
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 t…
Turán-type inequaities for generalized polygamma function
Omprakash Atale
Inspired by the work of C. Mortici [1] and A. Laforgia et. al [2] we have established some new Turán-type inequalities for k-polygamma function and p-k-polygamma function.
Analytic expressions for some Mellin transforms with their application to prime counting function and interpolation formulas for the zeta function
Omprakash Atale
The aim of our present work here is to present few results in the theory of Mellin transforms using the method that S. Ramanujan used in proving his Master Theorem. Further applica…
On certain extensions of Ramanujan's Master Theorem and their applications
Omprakash Atale, Mahendra Shirude
S. Ramanujan introduced a technique in 1913 for providing analytic expressions for certain Mellin-type integrals which is now known as Ramanujan's Master Theorem. This technique wa…