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.
Sums of Powers Integer Sequences Identities Creative Telescoping Harmonic Numbers
Birincil Dil | İngilizce |
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Bölüm | Makaleler |
Yazarlar | |
Yayımlanma Tarihi | 28 Aralık 2018 |
Yayımlandığı Sayı | Yıl 2018 Cilt: 9 |