IDENTITIES INVOLVING GENERALIZED BERNOULLI NUMBERS AND PARTIAL BELL POLYNOMIALS WITH THEIR APPLICATIONS
By
M. A. Pathan ¹, Hemant Kumar², J. L´opez-Bonilla³ and Hunar Sherzad Taher ⁴ ¹
¹Centre for Mathematical and Statistical Sciences, Peechi Campus, Peechi, Kerala, India-680653
Department of Mathematics, Aligarh Muslim University, Aligarh, Uttar Pradesh, India-202002
²Department of Mathematics, D. A-V. Postgraduate College, Kanpur, Uttar Pradesh, India-208001
³ESIME-Zacatenco, Instituto Polit´ecnico Nacional, Edif. 4, 1er. Piso, Col. Lindavista CP, CDMX, Mexico-07738
⁴Department of Mathematics, University of Salahaddin, Erbil, Iraq-44001
Email: mapathan@gmail.com, palhemant2007@rediffmail.com, jlopezb@ipn.mx, hunar.taher@su.edu.krd
(Received: February 22, 2023; In format: February 25, 2023; Revised : May 25, 2023;Accepted : June 03, 2023)
DOI: https://doi.org/10.58250/jnanabha.2023.53132
Abstract
In the present paper, we show that the partial Bell polynomials allow for obtaining identities involving the generalized Bernoulli numbers. Then, on applying these identities we derive different generating and bilateral generating functions.
2020 Mathematical Sciences Classification: 05A15, 05A19, 05A30.
Keywords and Phrases: Bernoulli polynomials, Partial Bell polynomials, Generalized Bernoulli numbers, Generating and bilateral generating functions.