- Turkish Journal of Mathematics and Computer Science
- Vol: 9
- A Generalization of Ibn Al-Haytham Recursive Formula for Sums of Powers
A Generalization of Ibn Al-Haytham Recursive Formula for Sums of Powers
Authors : Hossein TEİMOORİ FAAL
Pages : 25-33
View : 6 | Download : 3
Publication Date : 2018-12-28
Article Type : Research
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