Results 21 to 30 of about 6,487,913 (78)
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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Generalizations of the Lerch zeta function. [PDF]
The Lerch zeta function is a three-variable generalization of the Riemann zeta function and the Hurwitz zeta function. In this thesis, we study generalizations and analogues of the Lerch zeta function. Our approaches proceed along three directions: local,
Ngo, Hieu T.
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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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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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, 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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Expansion formulas for an extended Hurwitz-Lerch zeta function obtained via fractional calculus [PDF]
Advances in Difference Equations, 2014 AbstractMotivated by the recent investigations of several authors, in this paper, we derive several new expansion formulas involving a generalized Hurwitz-Lerch zeta function introduced and studied recently by Srivastavaet al. (Integral Transforms Spec. Funct. 22:487-506, 2011).
Srivastava, Hari +2 more
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A Series Representation for the Hurwitz–Lerch Zeta Function
, 2021 We derive a new formula for the Hurwitz–Lerch zeta function in terms of the infinite sum of the incomplete gamma function.
Robert Reynolds, Allan Stauffer
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Vanishing of the integral of the Hurwitz zeta function [PDF]
, 2002 A proof is given that the improper Riemann integral of δ(s, a) with respect to the real parameter a, taken over the interval (0, 1], vanishes for all complex s with R(s) < 1.
Kevin A. Broughan, Broughan, Kevin A.
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Sum of the Hurwitz-Lerch Zeta Function over Natural Numbers: Derivation and Evaluation
, 2022 We consider a Hurwitz-Lerch zeta function Φs,z,a sum over the natural numbers. We provide an analytically continued closed form solution for this sum in terms of the addition of Hurwitz-Lerch zeta functions.
Robert Reynolds, Allan Stauffer
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New Expansion Formulas for a Family of the λ‐Generalized Hurwitz‐Lerch Zeta Functions
International Journal of Mathematics and Mathematical Sciences, Volume 2014, Issue 1, 2014., 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). These expansion formulas are obtained by making use of some important fractional calculus theorems such as the generalized Leibniz rules, the Taylor‐like expansions in terms of different functions, and ...
H. M. Srivastava +2 more
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