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 ofpowers 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 likeKaraji L-summing equation and Abel's summation by parts lemma. Finally, as an application, we prove several identities related to Fibonnaci and harmonic numbers.