Hossein Teimoori Faal

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

ISSN: 2148-1830
Yayın Aralığı: 2
Başlangıç: 2013
Yayıncı: MATEMATİKÇİLER DERNEĞİ

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

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