ON THE TAYLOR EXPANSION OF (−zg(q); f(q))∞
By
M. A. Pathan1* , J. D. Bulnes2 , H. Kumar3 and J. L´opez-Bonilla4
1Centre for Mathematical and Statistical Sciences, Peechi Campus, Peechi, Kerala, India-680 653
*Department of Mathematics, Aligarh Muslim University, Aligarh, Uttar Pradesh, India-202002;
2Departamento de Ciencias Exatas e Tecnolog´ıa, Universidade Federal do Amap´a, Rod. Juscelino Kubitschek, Jardin Marco Zero, Macap´a, AP, Brasil-68903-419; bulnes@unifap.br
3Department of Mathematics, D. A-V. Postgraduate College, Kanpur, Uttar Pradesh, India-208 001
4ESIME-Zacatenco, Instituto Polit´ecnico Nacional, Edif. 4, 1er. Piso, Col. Lindavista CP, CDMX, M´exico-07738.
Email: mapathan@gmail.com, palhemant2007@rediffmail.com; hemantkumar kn03@csjmu.ac.in, jlopezb@ipn.mx
(Received: March 11, 2025; In format: March 14, 2025; Revised: June 14, 2025; Accepted: March 14, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55124
Abstract
The Leverrier-Takeno process allows to construct the characteristic polynomial of a matrix; here we employ this method to obtain the Taylor expansion of (−zg(q); f(q))∞, with special interest in (−zq; q2 )∞ because it participates in the Jacobi triple product identity.
2020 Mathematical Sciences Classification: 05A17, 11C08, 11C20, 11B73, 33D15
Keywords and Phrases: Characteristic polynomial, Leverrier-Takeno’s procedure, Complete Bell polynomials, Partition function, Newton’s recurrence expression, q-series, Jacobi triple product identity, Taylor expansion.