Results 11 to 20 of about 864 (74)
New Expansion Formulas for a Family of the λ-Generalized Hurwitz-Lerch Zeta Functions
International Journal of Mathematics and Mathematical Sciences, 2014 We derive several new expansion formulas for a new family of the λ-generalized Hurwitz-Lerch zeta functions which were introduced by Srivastava (2014).
H. M. Srivastava, Sébastien Gaboury
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New result of analytic functions related to Hurwitz zeta function. [PDF]
ScientificWorldJournal, 2013 By using a linear operator, we obtain some new results for a normalized analytic function f defined by means of the Hadamard product of Hurwitz zeta function. A class related to this function will be introduced and the properties will be discussed.
Ghanim F, Darus M.
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Aspects of the screw function corresponding to the Riemann zeta‐function
Journal of the London Mathematical Society, Volume 108, Issue 4, Page 1448-1487, October 2023., 2023 Abstract We introduce a screw function corresponding to the Riemann zeta‐function and study its properties from various aspects. Typical results are several equivalent conditions for the Riemann hypothesis in terms of the screw function. One of them can be considered an analog of so‐called Weil's positivity or Li's criterion.
Masatoshi Suzuki
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A Double Integral Containing the Fresnel Integral Function S(x): Derivation and Computation
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 A two‐dimensional integral containing S(x) is derived. S(x) is the Fresnel integral function, and the double integral is taken over the range 0 < x < ∞ and 0 < y < ∞. A representation in terms of the Hurwitz–Lerch zeta function is derived, from which other special function representations can be evaluated. All the results in this work are new.
Robert Reynolds +2 more
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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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Integral expressions for Hilbert-type infinite multilinear form and related multiple Hurwitz-Lerch Zeta functions [PDF]
, 2012 The article deals with different kinds integral expressions concerning multiple Hurwitz-Lerch Zeta function (introduced originally by Barnes ), Hilbert-type infinite multilinear form and its power series extension.
Ram K. Saxena, Tibor Pogany
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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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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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The Lerch Zeta Function II. Analytic Continuation [PDF]
, 2010 This is the second of four papers that study algebraic and analytic structures associated with the Lerch zeta function. In this paper we analytically continue it as a function of three complex variables.
Apostol T. M. +7 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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