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Analytic study and statistical enforcement of extended beta functions imposed by Mittag-Leffler and Hurwitz-Lerch Zeta functions [PDF]

MethodsX
Special Function Theory is used in many mathematical fields to model scientific progress, from theoretical to practical. This helps efficiently analyze the newly expanded Beta class of functions on a complicated domain.
Faten F. Abdulnabi, Hiba F. Al-Janaby, Firas Ghanim   +2 more
doaj   +2 more sources

New extensions of associated Laguerre polynomials [PDF]

E-Journal of Analysis and Applied Mathematics, 2020
The main object of this paper is to present new extensions of associated Laguerre polynomials. Some integral representations, recurrence relations, generating functions and summation formulae are obtained for these new extended Laguerre polynomials.
Ahmed Ali Al-Gonah
doaj   +1 more source

Summation Formulae for Quintic q-Series

Mathematics, 2022
By utilizing the modified Abel lemma on summation by parts, we examine a class of quintic q-series, that have close connections to the “twisted cubic q-series”. Several remarkable summation and transformation formulae are established.
Wenchang Chu
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Some Generalized Properties of Poly-Daehee Numbers and Polynomials Based on Apostol–Genocchi Polynomials

Mathematics, 2022
Numerous polynomial variations and their extensions have been explored extensively and found applications in a variety of research fields. The purpose of this research is to establish a unified class of Apostol–Genocchi polynomials based on poly-Daehee ...
Talha Usman, Nabiullah Khan, Mohd Aman, Shrideh Al-Omari, Kamsing Nonlaopon, Junesang Choi   +5 more
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Four Variants of Riemann Zeta Function

Mathematics, 2022
By means of the generating function method and Dougall’s formulae for bilateral hypergeometric series, we examine four classes of infinite series, which may be considered as variants of Riemann zeta function. Several summation formulae are established in
Nadia N. Li, Wenchang Chu
doaj   +1 more source

Around the Lipschitz Summation Formula [PDF]

Mathematical Problems in Engineering, 2020
Boundary behavior of important functions has been an object of intensive research since the time of Riemann. Kurokawa, Kurokawa-Koyama, and Chapman studied the boundary behavior of generalized Eisenstein series which falls into this category. The underlying principle is the use of the Lipschitz summation formula.
Wenbin Li, Hongyu Li, Jay Mehta
openaire   +2 more sources

Properties of Multivariable Hermite Polynomials in Correlation with Frobenius–Genocchi Polynomials

Mathematics, 2023
The evolution of a physical system occurs through a set of variables, and the problems can be treated based on an approach employing multivariable Hermite polynomials.
Shahid Ahmad Wani, Georgia Irina Oros, Ali M. Mahnashi, Waleed Hamali   +3 more
doaj   +1 more source

Summation formulas of q-hyperharmonic numbers [PDF]

Afrika Matematika, 2021
Afrika ...
Komatsu, Takao, Li, Rusen
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A Parametric Kind of Fubini Polynomials of a Complex Variable

Mathematics, 2020
In this paper, we propose a parametric kind of Fubini polynomials by defining the two specific generating functions. We also investigate some analytical properties (for example, summation formulae, differential formulae and relationships with other well ...
Sunil Kumar Sharma, Waseem A. Khan, Cheon Seoung Ryoo   +2 more
doaj   +1 more source

Harmonic number identities via polynomials with r-Lah coefficients

Comptes Rendus. Mathématique, 2020
In this paper, polynomials whose coefficients involve $r$-Lah numbers are used to evaluate several summation formulae involving binomial coefficients, Stirling numbers, harmonic or hyperharmonic numbers.
Kargın, Levent, Can, Mümün
doaj   +1 more source