CONNECTION BETWEEN PARTIAL BELL POLYNOMIALS AND \boldmath$(q ; q)_{k}$; PARTITION FUNCTION, AND CERTAIN \boldmath$ q $-HYPERGEOMETRIC SERIES

M. A. Pathan; J. D. Bulnes; J. L'opez-Bonilla; Hemant Kumar

doi:https://doi.org/10.56827/JRSMMS.2022.1001.1

M. A. Pathan Centre for Mathematical and Statistical Sciences, Peechi Campus, Peechi - 680653, Kerala, INDIA

J. D. Bulnes Departamento de Ciencias Exatas e Tecnologia, Universidade Federal do Amapa, Rod. Juscelino Kubitschek, Jardin Marco Zero, 68903-419, Macapa, AP, BRAS

J. L'opez-Bonilla ESIME-Zacatenco, Instituto Politecnico Nacional, Edif. 4, 1er. Piso, Col. Lindavista 07738 CDMX, MEXICO

Hemant Kumar Department of Mathematics, D. A-V. Postgraduate College, Kanpur - 208001, (U.P.), INDIA

Volume 10, Issue 1 Pages 1-12 December 30, 2022 380 downloads

Article overview

Abstract

We exhibit a relationship between $q$-shifted factorial, $(q ; q)_{n}$, and the incomplete exponential Bell polynomials and also evaluate several $q$-hypergeometric series using the $q$-version of Petkovsek-WilfZeilberger's algorithm. Finally, we write the partition function $p(n)$ in terms of $Q_{m}(k)$, the number of partitions of $m$ using (possibly repeated) parts that do not exceed $k$.

Keywords and Phrases

Partial Bell polynomials$q$-analysisHessenberg determinant$q$-Hypergeometric series$q$-Petkovsek-Wilf-Zeilberger's techniquesPartition functions.

AMS Subject Classification

33D90, 33D70.

Reference information

How to Cite

M. A. Pathan, J. D. Bulnes, J. L'opez-Bonilla, Hemant Kumar (2022). CONNECTION BETWEEN PARTIAL BELL POLYNOMIALS AND \boldmath$(q ; q)_{k}$; PARTITION FUNCTION, AND CERTAIN \boldmath$ q $-HYPERGEOMETRIC SERIES. Journal of Ramanujan Society of Mathematics and Mathematical Sciences, 10(1), 1-12.

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