• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.305-319
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• 2017

Recently many authors have investigated so-called Aleph (${\aleph}$)-function and its various properties. Here, in this paper, we aim at establishing certain integral formulas involving the Aleph (${\aleph}$)-function. Precisely, integrals with product of Aleph (${\aleph}$)-function with Jacobi polynomials, Bessel Maitland function, general class of polynomials were under consideration. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones.

• Honam Mathematical Journal
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• v.41 no.1
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• pp.1-17
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• 2019

The aim of this paper is to establish certain integrals involving product of the Aleph function with exponential function and multi Gauss's hypergeometric function. Being unified and general in nature, these integrals yield a number of known and new results as special cases. For the sake of illustration, twelve corollaries are also recorded here as special case of our main results.

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.373-386
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• 2023

In this paper we have obtained various forms of (p, q)-analogue of Aleph-Function satisfying Truesdell's ascending and descending F_p,q-equation. These structures have been employed to arrive at certain generating functions for (p, q)-analogue of Aleph-Function. Some specific instances of these outcomes as far as (p, q)-analogue of I-function, H-function and G-functions have likewise been obtained.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.465-471
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• 2016

In this paper, we establish certain integrals involving Srivastava's Polynomials [5] and Aleph Function ([8], [10]). On account of general nature of the functions and polynomials involved in the integrals, our results provide interesting unifications and generalizations of a large number of new and known results, which may find useful applications in the field of science and engineering. To illustrate, we have recorded some special cases of our main results which are also sufficiently general and unified in nature and are of interest in themselves.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.343-371
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• 2007

We find the super-replication formulae which would be a generalization of replication formulae. And we apply the formulae to derive periodically vanishing property in the Fourier coefficients of the Hauptmodul $\aleph(j_{1,N})$ as a super-replicable function.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.381-392
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• 2021

During the last several decades, a great variety of fractional kinetic equations involving diverse special functions have been broadly and usefully employed in describing and solving several important problems of physics and astrophysics. In this paper, we aim to find solutions of a type of fractional kinetic equations associated with the (p, q)-extended 𝜏 -hypergeometric function and the (p, q)-extended 𝜏 -confluent hypergeometric function, by mainly using the Laplace transform. It is noted that the main employed techniques for this chosen type of fractional kinetic equations are Laplace transform, Sumudu transform, Laplace and Sumudu transforms, Laplace and Fourier transforms, P_𝛘-transform, and an alternative method.