CONNECTION BETWEEN PARTIAL BELL POLYNOMIALS AND (q; q)k; PARTITION FUNCTION, AND CERTAIN q-HYPERGEOMETRIC SERIE

Authors

  • 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)

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 Qm(k), the number of partitions of m using (possibly repeated) parts that do not exceed k.

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Published

2023-06-08

Issue

Vol. 10 No. 01 (2022): Journal of Ramanujan Society of Mathematics and Mathematical Sciences

Section

Articles