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3 articles for “Mellin transforms”
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On the Formula for Distribution of Prime Numbers
Abstract: The detailed derivation of the distribution of prime numbers, the research result originally presented in the 2013’ monograph Study of Analytic Number Theory: Riemann’s Hypothesis and Prime Number Theorem with Addendum on Integer Partitions published with Cam- bridge International Science Publishing, is once again presented in this paper with the purpose to give an insight to unfamiliar authors.
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 1, Issue 1, 2014 · pp. 16–19 Read article
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On the Riemann Hypothesis in The Light of The Littlewood Criterion of Equivalence
Abstract: In 1859, Riemann extended the Euler study onto the case of a complex variable according to then new Cauchy's complex analysis. According to his point of view, all non-trivial zeros of the Riemann zeta function are located on the critical line s=1/2+it, where t is a real number. In 1912, Littlewood presented the equivalence criterion for the Riemann Hypothesis based on the Mertens function. In this paper, the Riemann Hypothesis …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 1, Issue 2, 2014 · pp. 26–35 Read article
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The Relation between Double Laplace Transform and Double Hankel Transform with Applications II
Abstract: The object of this paper is to establish a relationship between the double Laplace transform and the double Hankel transform. A double Laplace-Hankel transform of the product of H-functions of one and two variables is then obtained. Application of our main result, summation formula and some interesting special cases have also been discussed. Keywords:Double Laplace transform, double Hankel transform, Mellin-Bernes contour integral, H-function
Published in Research & Reviews : Journal of Physics · Vol. 1, Issue 2, 2012 · pp. 19–25 Read article