✨
AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Finally, as anapplication, we prove several identities related to Fibonnaci and harmonic numbers.
📌 3 Key Takeaways
🎯
Objective & Hypothesis:In this paper, we give a sequential generalization of Ibn al-Haytham recursive formula for sums ofpowers of any integer sequence.
📊
Key Findings & Data:Then, we obtain a higher order dimensional generalization of the generalizedIbn al-Haytham formula.
💡
Conclusion & Impact:Finally, as anapplication, we prove several identities related to Fibonnaci and harmonic numbers.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
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.
🔖
Cite This Article
Faal, H. T. (2022). A Generalization of Ibn al-Haytham Recursive Formula for Sums of Powers. Turkish Journal of Mathematics and Computer Science, Cilt: 9 - Sayı: 9, 25–33. https://ajindex.com/articles/609176