Results 91 to 100 of about 2,188 (164)

``Almost'' universality of the Lerch zeta-function

open access: yesMathematical Communications, 2019
Summary: The Lerch zeta-function \(L(\lambda,\alpha,s)\) with transcendental parameter \(\alpha\), or with rational parameters \(\alpha\) and \(\lambda\) is universal, i.e., a wide class of analytic functions is approximated by shifts \(L(\lambda,\alpha,s+i\tau)\), \(\tau \in \mathbb{R}\). The case of algebraic irrational \(\alpha\) is an open problem.
openaire   +2 more sources

A new extension of Hurwitz-Lerch Zeta function

open access: yes, 2018
The main objective of this paper is to introduce a new extension of Hurwitz-Lerch Zeta function in terms of extended beta function. We then investigate its important properties such as integral representations, differential formulas, Mellin transform and certain generating relations.
Rahman, Gauhar   +2 more
openaire   +2 more sources

Joint discrete universality for Lerch zeta-functions

open access: yes, 2018
Summary: After \textit{S. M. Voronin}'s work of [Math. USSR, Izv. 9, 443--453 (1976); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 39, 475--486 (1975; Zbl 0315.10037)], it is known that some of zeta and \(L\)-functions are universal in the sense that their shifts approximate a wide class of analytic functions.
Laurinčikas, Antanas, Mincevič, Asta
openaire   +1 more source

Fuzzy Subordination Results for Meromorphic Functions Associated with Hurwitz–Lerch Zeta Function

open access: yesMathematics
The notion of the fuzzy set was incorporated into geometric function theory in recent years, leading to the emergence of fuzzy differential subordination theory, which is a generalization of the classical differential subordination notion.
Ekram E. Ali   +4 more
doaj   +1 more source

Approximation of analytic functions by generalized shifts of the Lerch zeta-function

open access: yesMathematical Modelling and Analysis
In the paper, we approximate analytic functions by generalized shifts of the Lerch zeta-function, where g is a certain increasing to real function having a monotonic derivative. We prove that, for arbitrary parameters λ and α, there exists a closed set  
Aidas Balčiūnas   +2 more
doaj   +1 more source

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