Submitted:
25 February 2021
Posted:
26 February 2021
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Abstract
We study various properties of the polygonal numbers; such as their recurrence relations; fundamental identities; weighted binomial and ordinary sums; partial sums and generating functions of their powers; and a continued fraction representation for them. 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; unlike what obtains in most literature.
Keywords:
polygonal number
; triangular number
; summation identity
; generating function
; partial sum
; recurrence relation
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