(w; β)-BELL POLYNOMIALS ∀w ∈ C, β > 0, THEIR APPLICATIONS IN IDENTITIES EVALUATION AND MATRIX EQUATION REPRESENTATION
By
R. C. Singh Chandel1 , Hemant Kumar2 and J. L´opez-Bonilla3
1Former Head Department of Mathematics, D. V. Postgraduate College, Orai, Uttar Pradesh, India-285001
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, M´exico-07738
Email: rc_chandel@yahoo.com, palhemant2007@rediffmail.com, jlopezb@ipn.mx
(Received: October 20, 2024; In format: October 25, 2024; Revised: November 30, 2024; Accepted: December 28, 2024)
DOI: https://doi.org/10.58250/jnanabha.2024.54234
Abstract
In the present paper on application of (w; β)-Bell polynomials ∀w ∈ C, β > 0, authors obtain identities of Kummer confluent hypergeometric function and Srivastava - Daoust function of two variables. Next they derive that the differentiation of these polynomials is connected with Stirling numbers of second kind. Also by these polynomials, they construct a matrix equation representation to study their analytic properties and diagonalization of a matrix consisting of these polynomials as its elements.
2020 Mathematical Sciences Classification: 11B73, 33C15, 33C20, 26A33.
Keywords: (w; β)-Bell polynomials, Stirling number of the second kind, contour integral, Kummer confluent hypergeometric function, Srivastava-Daoust function of two variables, matrix equation representation, Hadamard product.