Articles
Kyungpook Mathematical Journal 2018; 58(4): 599-613
Published online December 31, 2018
Copyright © Kyungpook Mathematical Journal.
On a Generalization of the Pentagonal Number Theorem
Ho-Hon Leung
Department of Mathematical Sciences, United Arab Emirates University, Al Ain, 15551, United Arab Emirates
e-mail : hohon.leung@uaeu.ac.ae
Received: April 3, 2018; Revised: August 20, 2018; Accepted: August 27, 2018
We study a generalization of the classical Pentagonal Number Theorem and its applications. We derive new identities for certain infinite series, recurrence relations and convolution sums for certain restricted partitions and divisor sums. We also derive new identities for Bell polynomials.
Keywords: integer partition, divisor sum, Bell polynomials, polygonal numbers, pentagonal number theorem.