Results 11 to 20 of about 462 (73)
New Relations Involving an Extended Multiparameter Hurwitz-Lerch Zeta Function with Applications [PDF]
International Journal of Analysis, 2014 We derive several new expansion formulas involving an extended multiparameter Hurwitz-Lerch zeta function introduced and studied recently by Srivastava et al. (2011). These expansions are obtained by using some fractional calculus methods such as the generalized Leibniz rules, the Taylor-like expansions in terms of different functions, and the ...
H. M. Srivastava +2 more
openaire +2 more sources
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
wiley +1 more source
Some Weighted Sum Formulas for Multiple Zeta, Hurwitz Zeta, and Alternating Multiple Zeta Values
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 We perform a further investigation for the multiple zeta values and their variations and generalizations in this paper. By making use of the method of the generating functions and some connections between the higher‐order trigonometric functions and the Lerch zeta function, we explicitly evaluate some weighted sums of the multiple zeta, Hurwitz zeta ...
Yuan He, Zhuoyu Chen, Li Guo
wiley +1 more source
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
wiley +1 more source
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
openaire +4 more sources
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
wiley +1 more source
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
openaire +2 more sources
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
wiley +1 more source
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
core +1 more source
Further generalization of the extended Hurwitz-Lerch Zeta functions
Boletim da Sociedade Paranaense de Matemática, 2017 Recently various extensions of Hurwitz-Lerch Zeta functions have been investigated. Here, we first introduce a further generalization of the extended Hurwitz-Lerch Zeta functions. Then we investigate certain interesting and (potentially) useful properties, systematically, of the generalization of the extended Hurwitz-Lerch Zeta functions, for example ...
Rakesh K. Parmar +2 more
openaire +4 more sources