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Estimates and properties of certain q-Mellin transform on generalized q-calculus theory
Advances in Difference Equations, 2021 This paper deals with the generalized q-theory of the q-Mellin transform and its certain properties in a set of q-generalized functions. Some related q-equivalence relations, q-quotients of sequences, q-convergence definitions, and q-delta sequences are ...
Shrideh Al-Omari
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New Inversion Techniques for Some Integral Transforms via the Generalized Product Theorem of the Mellin Transform [PDF]
, 2012 We introduce the generalized product theorem for the Mellin transform, and we solve certain classes of singular integral equations with kernels coincided with conditions of this theorem.
Alireza Ansari +1 more
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AxiomsThis paper presents a comprehensive study of Plancherel’s theorem and inversion formulae for the Widder–Lambert transform, extending its scope to Lebesgue integrable functions, compactly supported distributions, and regular distributions with compact ...
Emilio R. Negrín +2 more
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On the Relation between Lambert W-Function and Generalized Hypergeometric Functions
Stats, 2022 In the theory of special functions, finding correlations between different types of functions is of great interest as unifying results, especially when considering issues such as analytic continuation. In the present paper, the relation between Lambert W-
Pushpa Narayan Rathie +1 more
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Advances in Difference Equations, 2020 In this article, we investigate the so-called Inayat integral operator T p , q m , n $T_{p,q}^{m,n}$ , p , q , m , n ∈ Z $p,q,m,n\in \mathbb{Z}$ , 1 ≤ m ≤ q $1\leq m\leq q$ , 0 ≤ n ≤ p $0\leq n\leq p $ , on classes of generalized integrable functions. We
Shrideh Khalaf Al-Omari
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A NOTE ON THE AXISYMMETRIC DIFFUSION EQUATION [PDF]
The ANZIAM Journal, 2020 We consider the explicit solution to the axisymmetric diffusion equation. We recast the solution in the form of a Mellin inversion formula, and outline a method to compute a formula for $u(r,t)$ as a series using the Cauchy residue theorem.
A. E. Patkowski
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International Journal of Mathematics and Mathematical Sciences, 1988 A formula of inversion is established for an integral transform whose kernel is the Bessel function Ju(kr) where r varies over the finite interval (0,a) and the order u is taken to be the eigenvalue parameter.
D. Naylor
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New inversion, convolution and Titchmarsh's theorems for the half-Hilbert transform [PDF]
, 2013 While exploiting the generalized Parseval equality for the Mellin transform, we derive the reciprocal inverse operator in the weighted L2-space related to the Hilbert transform on the nonnegative half-axis.
S. Yakubovich
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A note on arithmetic Diophantine series [PDF]
Czechoslovak Mathematical Journal, 2018 We consider an asymptotic analysis for series related to the work of Hardy and Littlewood (1923) on Diophantine approximation, as well as Davenport. In particular, we expand on ideas from some previous work on arithmetic series and the RH.
A. E. Patkowski
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On Modified Mellin Transform of Generalized Functions
, 2013 We investigate the modified Mellin transform on certain function space of generalized functions. We first obtain the convolution theorem for the classical and distributional modified Mellin transform.
S. Al-Omari, Adem Kılıçman
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