Inequalities for Lerch transcendent function
نویسندگان
چکیده
Some fundamental inequalities for Lerch transcendent function with positive terms by utilising certain classical results due to Hölder, Čebyšev, Grüss and others, are established. particular cases of interest Polylogarithm function, Hurwitz zeta Legendre chi also given.
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 کاملGeometric Studies on Inequalities of Harmonic Functions in a Complex Field Based on ξ-Generalized Hurwitz-Lerch Zeta Function
Authors, define and establish a new subclass of harmonic regular schlicht functions (HSF) in the open unit disc through the use of the extended generalized Noor-type integral operator associated with the ξ-generalized Hurwitz-Lerch Zeta function (GHLZF). Furthermore, some geometric properties of this subclass are also studied.
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 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Tamkang Journal of Mathematics
سال: 2023
ISSN: ['0049-2930', '2073-9826']
DOI: https://doi.org/10.5556/j.tkjm.54.2023.3988