A Generalization of Ibn Al-Haytham Recursive Formula for Sums of Powers

Year 2018, Volume: 9, 25 - 33, 28.12.2018

Hossein Teimoori Faal

Abstract

In this paper, we give a generalization of Ibn al-Haytham recursive formula for sums of
powers of any integer sequence. Then, we obtain higher dimensional
generalizations of the generalized Ibn al-Haytham formula. As by-products, we also show that
how our recursive formulas imply other interesting integer sequences identities like
Karaji L-summing equation and Abel's summation by parts lemma. Finally,
as an application, we prove several identities related to Fibonnaci and harmonic numbers.

Keywords

Sums of Powers, Integer Sequences Identities, Creative Telescoping, Harmonic Numbers

References

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