منابع مشابه
Asymptotic behavior of the Lerch transcendent function
For complex parameters λ and s, consider the Lerch transcendent Φ(λ, s, z) = ∑∞ k=0 λ (k + z)−s as a function of the complex variable z. We analyze the asymptotic behavior of this function as Re s→ −∞.
متن کاملThe Lerch Transcendent from the Point of View of Fourier Analysis
We obtain some well-known expansions for the Lerch transcendent and the Hurwitz zeta function using elementary Fourier analytic methods. These Fourier series can be used to analytically continue the functions and prove the classical functional equations, which arise from the relations satisfied by the Fourier conjugate and flat Fourier series. In particular, the functional equation for the Riem...
متن کاملSimultaneous Polynomial Approximations of the Lerch Function
We construct bivariate polynomial approximations of the Lerch function, which for certain specialisations of the variables and parameters turn out to be HermitePadé approximants either of the polylogarithms or of Hurwitz zeta functions. In the former case, we recover known results, while in the latter the results are new and generalise some recent works of Beukers and Prévost. Finally, we make ...
متن کاملThe Lerch zeta function IV. Hecke operators
This paper studies algebraic and analytic structures associated with the Lerch zeta function. It defines a family of two-variable Hecke operators {Tm : m ≥ 1} given by Tm(f )(a, c) = 1 m ∑m−1 k=0 f ( a+k m ,mc) acting on certain spaces of real-analytic functions, including Lerch zeta functions for various parameter values. The actions of various related operators on these function spaces are de...
متن کاملRecurrence Relations for the Lerch Φ Function and Applications
Abstract. In this paper we present a simple method for deriving recurrence relations and we apply it to obtain two equations involving the Lerch Phi function and sums of Bernoulli and Euler polynomials. Connections between these results and those obtained by H.M. Srivastava, M.L. Glasser and V. Adamchik ([8]) are pointed out, emphasizing the usefulness of this approach with some meaningful exam...
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ژورنال
عنوان ژورنال: Mathematical Modelling and Analysis
سال: 2012
ISSN: 1392-6292,1648-3510
DOI: 10.3846/13926292.2012.662532