Submitted:
24 February 2021
Posted:
24 February 2021
Read the latest preprint version here
Abstract
We study various properties of the polygonal numbers; such as their recurrence relations, fundamental identities, weighted binomial and ordinary sums and the partial sums and generating functions of their powers. A feature of our results is that they are presented naturally in terms of the polygonal numbers themselves and not in terms of arbitrary integers as is the case in most literature.
Keywords:
polygonal number
; triangular number
; summation identity
; generating function
; partial sum
; recurrence relation
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