Results 1 to 10 of about 111 (90)
Series Representations at Special Values of Generalized Hurwitz-Lerch Zeta Function [PDF]
Abstract and Applied Analysis, 2013 By making use of some explicit relationships between the Apostol-Bernoulli, Apostol-Euler, Apostol-Genocchi, and Apostol-Frobenius-Euler polynomials of higher order and the generalized Hurwitz-Lerch zeta function as well as a new expansion formula for ...
S. Gaboury, A. Bayad
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Further Extension of the Generalized Hurwitz-Lerch Zeta Function of Two Variables [PDF]
Mathematics, 2019 The main aim of this paper is to provide a new generalization of Hurwitz-Lerch Zeta function of two variables. We also investigate several interesting properties such as integral representations, summation formula, and a connection with the generalized ...
Kottakkaran Sooppy Nisar
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Partial Sums of Generalized Class of Analytic Functions Involving Hurwitz-Lerch Zeta Function [PDF]
Abstract and Applied Analysis, 2011 Let fn(z)=z+∑k=2nakzk be the sequence of partial sums of the analytic function f(z)=z+∑k=2∞akzk. In this paper, we determine sharp lower bounds for ℜ{f(z)/fn(z)}, ℜ{fn(z)/f(z)}, ℜ{f′(z)/fn′(z)}, and ℜ{fn′(z)/f′(z)}.
G. Murugusundaramoorthy +2 more
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A note on a generalized double series. [PDF]
PLoS ONEBy employing contour integration the derivation of a generalized double finite series involving the Hurwitz-Lerch zeta function is used to derive closed form formulae in terms of special functions.
Robert Reynolds
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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.
europepmc +2 more sources
Sum of the Hurwitz‐Lerch Zeta Function over Natural Numbers: Derivation and Evaluation
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 We consider a Hurwitz‐Lerch zeta function Φ(s, 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. A new recurrence identity with consecutive neighbours and the product of trigonometric functions is derived.
Robert Reynolds +2 more
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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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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
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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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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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