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

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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