Results 41 to 50 of about 11,866,753 (228)
A Definite Integral Involving the Logarithmic Function in Terms of the Lerch Function
Mathematics, 2019 We present a method using contour integration to evaluate the definite integral of the form ∫ 0 ∞ log k ( a y ) R ( y ) d y in terms of special functions, where R ( y ) = y m 1 + α y n and k , m , a , α and n are arbitrary complex numbers.
Robert Reynolds, Allan Stauffer
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On a Certain Extension of the Hurwitz-Lerch Zeta Function
Annals of the West University of Timisoara: Mathematics and Computer Science, 2014 Our purpose in this paper is to consider a generalized form of the extended Hurwitz-Lerch Zeta function. For this extended Hurwitz-Lerch Zeta function, we obtain some classical properties which includes various integral representations, a differential ...
Parmar Rakesh K., Raina R. K.
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On zeros of the derivative of the Lerch zeta-function
Lietuvos Matematikos Rinkinys, 2002 We consider zeros of the derivative of the Lerch zeta-function. We obtain some lower bound for the number of zeros lying on the right from the critical line.
Ramūnas Garunkštis
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Exponential sums of Lerch’s zeta functions [PDF]
Proceedings of the American Mathematical Society, 1985 For x x not an an integer and Re ( s ) > 0 \operatorname {Re} (s) > 0 , let \[ F ( x , s ) = ∑ k = 1 ∞
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Finite Hurwitz-Lerch functions
Filomat, 2019 Summary: We define the finite Hurwitz-Lerch function \(\displaystyle H_n^{(s)}(x,y)= \sum_{k=0}^{n-1} \frac{x^k}{(k+y)^s}\). Then we explore some properties of them and give some applications, including Coppo's formula, the sum of powers of consecutive integers, Mellin differential operator, and some others.
Batir, Necdet, Chen, Kwang-Wu
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Series Representations at Special Values of Generalized Hurwitz-Lerch Zeta Function
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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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 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
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The Lerch zeta-function with algebraic irrational parameter
Lietuvos Matematikos Rinkinys, 2009 In this note, we present probabilisticlimit theorems on the complex plane as well as in functional spaces for the Lerch zeta-function with algebraic irrational parameter.
Danutė Genienė
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Two New Proofs of Lerch's Functional Equation [PDF]
Proceedings of the American Mathematical Society, 1972 One bright Sunday morning I went to church, And there I met a man named Lerch. We both did sing in jubilation, For he did show me a new equation. Two simple derivations of the functional equation of \[ ∑ n = 0 ∞ exp [ 2
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