Results 31 to 40 of about 300 (129)
Ural Mathematical Journal, 2022 With a possible connection to integrals used in General Relativity, we used our contour integral method to write a closed form solution for a quadruple integral involving exponential functions and logarithm of quotient radicals.
Robert Reynolds, Allan Stauffer
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The Mellin Transform of Logarithmic and Rational Quotient Function in terms of the Lerch Function
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 Upon reading the famous book on integral transforms volume II by Erdeyli et al., we encounter a formula which we use to derive a Mellin transform given by ∫0∞xm−1logkax/β2+x2γ+xdx, where the parameters a, k, β, and γ are general complex numbers. This Mellin transform will be derived in terms of the Lerch function and is not listed in current literature
Robert Reynolds +2 more
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, 2021 Fractional kinetic equations (FKEs) comprising a large array of special functions have been extensively and successfully applied in specification and solving many significant problems of astrophysics and physics.
Yağcı, Oğuz
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Leaf-to-leaf distances and their moments in finite and infinite m-ary tree graphs [PDF]
, 2015 We study the leaf-to-leaf distances on full and complete m-ary graphs using a recursive approach. In our formulation, leaves are ordered along a line. We find explicit analytical formulae for the sum of all paths for arbitrary leaf-to-leaf distance r as
Römer, Rudolf A. +2 more
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On extended Hurwitz–Lerch zeta function
Journal of Mathematical Analysis and Applications, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Luo, Min-Jie +2 more
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Twisted Eisenstein series, cotangent‐zeta sums, and quantum modular forms
Transactions of the London Mathematical Society, Volume 7, Issue 1, Page 33-48, December 2020., 2020 Abstract We define twisted Eisenstein series Es±(h,k;τ) for s∈C, and show how their associated period functions, initially defined on the upper half complex plane H, have analytic continuation to all of C′:=C∖R⩽0. We also use this result, as well as properties of various zeta functions, to show that certain cotangent‐zeta sums behave like quantum ...
Amanda Folsom
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Asymptotic expansions of the Hurwitz–Lerch zeta function
Journal of Mathematical Analysis and Applications, 2004 In the paper, a generalization of the asymptotic expansions obtained by \textit{M.~Katsurada} [Proc.~Japan Acad. 74, No. 10, 167--170 (1998; Zbl 0937.11035)] and \textit{D.~Klusch} [J.~Math. Anal. Appl. 170, No. 2, 513--523 (1992; Zbl 0763.11036)] for the Lipschitz-Lerch zeta function \[ R(a, x, s)\equiv\sum_{k=0}^\infty {e^{2k\pi ix}\over (a+k)^s ...
Ferreira, Chelo, López, José L.
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Around the Lipschitz Summation Formula
Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 Boundary behavior of important functions has been an object of intensive research since the time of Riemann. Kurokawa, Kurokawa‐Koyama, and Chapman studied the boundary behavior of generalized Eisenstein series which falls into this category. The underlying principle is the use of the Lipschitz summation formula.
Wenbin Li +3 more
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A Generalization of the Secant Zeta Function as a Lambert Series
Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 Recently, Lalín, Rodrigue, and Rogers have studied the secant zeta function and its convergence. They found many interesting values of the secant zeta function at some particular quadratic irrational numbers. They also gave modular transformation properties of the secant zeta function.
H.-Y. Li +3 more
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A New Family of the λ-Generalized Hurwitz-Lerch Zeta Functions with Applications [PDF]
, 2014 : Motivated largely by a number of recent investigations, we introduce and investigate the various properties of a certain new family of the λ-generalized Hurwitz-Lerch zeta functions.
H. M. Srivastava, M. Srivastava, H.
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