Results 11 to 20 of about 2,163 (157)
Sum of the Hurwitz-Lerch Zeta Function over Natural Numbers: Derivation and Evaluation
Journal of Mathematics, 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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Some Weighted Sum Formulas for Multiple Zeta, Hurwitz Zeta, and Alternating Multiple Zeta Values
Journal of Mathematics, 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 ...
Yuan He, Zhuoyu Chen
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A Double Integral Containing the Fresnel Integral Function Sx: Derivation and Computation
Journal of Mathematics, 2022 A two-dimensional integral containing Sx is derived.
Robert Reynolds, Allan Stauffer
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On Discrete Approximation of Analytic Functions by Shifts of the Lerch Zeta Function
Mathematics, 2022 The Lerch zeta function is defined by a Dirichlet series depending on two fixed parameters. In the paper, we consider the approximation of analytic functions by discrete shifts of the Lerch zeta function, and we prove that, for arbitrary parameters and a
Audronė Rimkevičienė +1 more
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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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Mechanochemical synthesis and crystal structure evaluation of Na2ZnSnS4
Zeitschrift für anorganische und allgemeine Chemie, Volume 648, Issue 23, December 13, 2022., 2022 Abstract Phase‐pure and highly crystalline Na2ZnSnS4 was prepared via a mechanochemical synthesis route. It crystallizes in the kesterite‐type structure. The unusual large Debye‐Waller factors of the sodium atoms were analyzed in detail, respecting also group‐theoretical aspects.
Eva M. Heppke +2 more
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A Series Representation for the Hurwitz–Lerch Zeta Function
Axioms, 2021 We derive a new formula for the Hurwitz–Lerch zeta function in terms of the infinite sum of the incomplete gamma function. Special cases are derived in terms of fundamental constants.
Robert Reynolds, Allan Stauffer
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The Lerch zeta function I. Zeta integrals [PDF]
Forum Mathematicum, 2012 Abstract. This is the first of four papers that study algebraic and analytic structures associated to the Lerch zeta function. This paper studies “zeta integrals” associated to the Lerch zeta function using test functions, and obtains functional equations for them.
Lagarias, Jeffrey C. +1 more
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Two New Generalizations of Extended Bernoulli Polynomials and Numbers, and Umbral Calculus
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 Among a remarkably large number of various extensions of polynomials and numbers, and diverse introductions of new polynomials and numbers, in this paper, we choose to introduce two new generalizations of some extended Bernoulli polynomials and numbers by using the Mittag–Leffler function and the confluent hypergeometric function.
Nabiullah Khan +4 more
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The false theta functions of Rodgers and their modularity
Bulletin of the London Mathematical Society, Volume 53, Issue 4, Page 963-980, August 2021., 2021 Abstract In this survey article, we explain how false theta functions can be embedded into a modular framework and show some of the applications of this modularity.
Kathrin Bringmann
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