scholarly journals Finite Integral Involving the Modified Generalized Aleph-Function of Two Variables Extension and Generalized Extented Hurwitz’s Zeta Function

2021 ◽  
Vol 8 (5) ◽  
pp. 198-212
Author(s):  
Frédéric Ayant ◽  
Prvindra Kumar
Keyword(s):  
Zeta Function ◽  
Finite Integral ◽  
Function Of Two Variables ◽  
Generalized Zeta Function

In the present paper, we evaluate the general finite integral invoving the generalized Zeta function and the modified of generalized Aleph-function of two variables.

scholarly journals Note on the Hurwitz–Lerch Zeta Function of Two Variables

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1431
Author(s):  
Junesang Choi ◽  
Recep Şahin ◽  
Oğuz Yağcı ◽  
Dojin Kim
Keyword(s):  
Zeta Function ◽  
Generating Functions ◽  
Recurrence Relations ◽  
Zeta Functions ◽  
Integral Representations ◽  
Lerch Zeta Function ◽  
Derivative Formulas ◽  
The One ◽  
Function Of Two Variables

A number of generalized Hurwitz–Lerch zeta functions have been presented and investigated. In this study, by choosing a known extended Hurwitz–Lerch zeta function of two variables, which has been very recently presented, in a systematic way, we propose to establish certain formulas and representations for this extended Hurwitz–Lerch zeta function such as integral representations, generating functions, derivative formulas and recurrence relations. We also point out that the results presented here can be reduced to yield corresponding results for several less generalized Hurwitz–Lerch zeta functions than the extended Hurwitz–Lerch zeta function considered here. For further investigation, among possibly various more generalized Hurwitz–Lerch zeta functions than the one considered here, two more generalized settings are provided.

scholarly journals Further Extension of the Generalized Hurwitz-Lerch Zeta Function of Two Variables

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 48
Author(s):  
Kottakkaran Sooppy Nisar
Keyword(s):  
Zeta Function ◽  
Hypergeometric Function ◽  
Summation Formula ◽  
Integral Representations ◽  
Generalized Hypergeometric Function ◽  
Special Cases ◽  
Lerch Zeta Function ◽  
Function Of Two Variables

The main aim of this paper is to provide a new generalization of Hurwitz-Lerch Zeta function of two variables. We also investigate several interesting properties such as integral representations, summation formula, and a connection with the generalized hypergeometric function. To strengthen the main results we also consider some important special cases.

scholarly journals ONE-LOOP QUANTUM COSMOLOGICAL CORRECTION TO THE GRAVITATIONAL CONSTANT IN THE CLOSED FRIEDMANN–ROBERTSON–WALKER UNIVERSE

2010 ◽  
Vol 25 (21) ◽  
pp. 4111-4122
Author(s):  
S. JALALZADEH ◽  
F. DARABI
Keyword(s):  
Zeta Function ◽  
Regularization Method ◽  
Gravitational Constant ◽  
Invariance Property ◽  
Shape Invariance ◽  
The One ◽  
Friedmann Robertson Walker ◽  
Fluctuation Potential ◽  
Generalized Zeta Function

In this paper, we calculate the one-loop quantum cosmological corrections to the kink energy in the closed Friedmann–Robertson–Walker universe in which the fluctuation potential V″ has a shape invariance property. We use the generalized zeta-function regularization method to implement our setup for describing quantum kink-like states. It is conjectured that the corrections lead to the renormalized gravitational constant.

scholarly journals Hurwitz Zeta Function of Two Variables and Associated Properties

2020 ◽  
pp. 297-315
Author(s):  
M. A. Pathan ◽  
Maged G. Bin-Saad ◽  
J. A. Younis
Keyword(s):  
Zeta Function ◽  
Integral Representations ◽  
Hurwitz Zeta Function ◽  
Summation Formulas ◽  
Lerch Zeta Function ◽  
Function Of Two Variables

The main objective of this work is to introduce a new generalization of Hurwitz-Lerch zeta function of two variables. Also, we investigate several interesting properties such as integral representations, operational connections and summation formulas.

scholarly journals The Zeta Function of a Hypergraph

10.37236/1110 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Christopher K. Storm
Keyword(s):  
Zeta Function ◽  
Riemann Hypothesis ◽  
Bipartite Graphs ◽  
Selberg Zeta Function ◽  
Isomorphic Graphs ◽  
Natural Way ◽  
Generalized Zeta Function

We generalize the Ihara-Selberg zeta function to hypergraphs in a natural way. Hashimoto's factorization results for biregular bipartite graphs apply, leading to exact factorizations. For $(d,r)$-regular hypergraphs, we show that a modified Riemann hypothesis is true if and only if the hypergraph is Ramanujan in the sense of Winnie Li and Patrick Solé. Finally, we give an example to show how the generalized zeta function can be applied to graphs to distinguish non-isomorphic graphs with the same Ihara-Selberg zeta function.

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