SUMS OF THE POWERS OF
RECIPROCALS OF POLYGONAL NUMBERS
Sameen Ahmed Khan
Department of Mathematics and Sciences
College of Arts and Applied Sciences
Dhofar University
Salalah - 211, Sultanate of OMAN

Abstract

We address the question of expressing the sums of the powers of polygonal numbers in closed forms using some basic functions. We obtain explicit expressions for the closed form expressions for the sums of the squares of reciprocals of polygonal numbers, the sums of the cubes of reciprocals of polygonal numbers the sums of the fourth-powers of reciprocals of polygonal numbers. These closed form expressions are composed of digamma function, Riemann zeta function and the Hurwitz zeta function. It has been possible to obtain the general result for the sums of an arbitrary power of reciprocals of square numbers. An outline is given to extend the result to the general case of the sums of the powers of reciprocals of polygonal numbers.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 33
Issue: 2
Year: 2020

DOI: 10.12732/ijam.v33i2.6

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