Results 31 to 40 of about 146 (114)
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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Applications ~of $Q$-hypergeometric and Hurwitz-Lerch Zeta Functions on Meromorphic Functions [PDF]
Mathematics Interdisciplinary Research, 2023 A new subclass of meromorphic univalent functions by using the q-hypergeometric and Hurwitz-Lerch Zeta functions is defined. Also, by applying the generalized Liu-Srivastava operator on meromorphic functions, some geometric properties of the new ...
Seyed Hadi Sayedain Boroujeni +1 more
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Real zeros of Hurwitz–Lerch zeta and Hurwitz–Lerch type of Euler–Zagier double zeta functions [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2015 AbstractLet 0 < a ⩽ 1, s, z ∈ ${\mathbb{C}}$ and 0 < |z| ⩽ 1. Then the Hurwitz–Lerch zeta function is defined by Φ(s, a, z) ≔ ∑∞n = 0zn(n + a)− s when σ ≔ ℜ(s) > 1. In this paper, we show that the Hurwitz zeta function ζ(σ, a) ≔ Φ(σ, a, 1) does not vanish for all 0 < σ < 1 if and only if a ⩾ 1/2.
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Fourier expansion and integral representation generalized Apostol-type Frobenius–Euler polynomials
Advances in Difference Equations, 2020 The main purpose of this paper is to investigate the Fourier series representation of the generalized Apostol-type Frobenius–Euler polynomials, and using the above-mentioned series we find its integral representation.
Alejandro Urieles +3 more
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Remark on the Hurwitz-Lerch zeta function [PDF]
Fixed Point Theory and Applications, 2013 By the Poisson summation formula, relating a function with its Fourier coefficients, the author obtaines the analytic continuation and a functional relation for a certain Lerch zeta function. The author also deduces \textit{T. M. Apostol}'s result [Pac. J. Math. 1, 161--167 (1951; Zbl 0043.07103)] about the Lerch zeta function and a functional relation
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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
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Applications of the Hurwitz-Lerch Zeta-Function [PDF]
Pure and Applied Mathematics Journal, 2015 In this paper, we shall exhibit the use of two principles, “principle of decomposition into residue classes” and “binomial principle of analytic continuation” due to Ram Murty and Sinha and indicate a certain distribution property and the functional equation for the Lipschitz-Lerch transcendent at integral arguments ofs.
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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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Series of Floor and Ceiling Functions—Part II: Infinite Series
Mathematics, 2022 In this part of a series of two papers, we extend the theorems discussed in Part I for infinite series. We then use these theorems to develop distinct novel results involving the Hurwitz zeta function, Riemann zeta function, polylogarithms and Fibonacci ...
Dhairya Shah +4 more
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Some formulas related to Hurwitz–Lerch zeta functions [PDF]
The Ramanujan Journal, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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