Results 11 to 20 of about 111 (90)
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
wiley +1 more source
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
doaj +1 more source
On the generalized Hurwitz-Lerch zeta function and generalized Lambert transform [PDF]
Journal of Classical Analysis, 2020 Summary: \textit{R. K. Raina} and \textit{H. M. Srivastava} [Rev. Téc. Fac. Ing., Univ. Zulia 18, No. 3, 301--304 (1995; Zbl 0851.11052)] introduced a generalized Lambert transform. \textit{S. P. Goyal} and \textit{R. K. Laddha} [Gaṇita Sandesh 11, No.
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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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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 study of generalized Hurwitz–Lerch zeta function and fractional kinetic equations
Research in MathematicsSaddam Husain +2 more
exaly +2 more sources
An extension of the generalized Hurwitz-Lerch Zeta function of two variables
Filomat, 2017 The main object of this paper is to introduce a new extension of the generalized Hurwitz-Lerch Zeta functions of two variables. We then systematically investigate such its several interesting properties and related formulas as (for example) various integral representations, which provide certain new and known extensions of earlier ...
Choi, Junesang, Parmar, Rakesh K.
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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
wiley +1 more source