Journals / Turkish Journal of Mathematics and Computer Science / 2021 / Cilt: 13 - Sayı: 1

Karaji's L-Summing Method and the Generalized Ibn al-Haytham Recursive Formula

Pages
122–128
Publication Date
2022-11-02
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we will also show the interplay between these two different methodsof summation.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we first review two folkloric summation techniquesdue to two Islamic medieval scholars Karaji and Ibn al-Haytham by emphasizing on their higher-dimensional extensions.
📊
Key Findings & Data:We also include several interesting examples of algebraic identities obtained form the generalized Ibn al-Haytham formulas and Karaji'sL-summing method.
💡
Conclusion & Impact:Finally, we will also show the interplay between these two different methodsof summation.
🔬Design:Review & Systematic Survey
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, we first review two folkloric summation techniquesdue to two Islamic medieval scholars Karaji and Ibn al-Haytham by emphasizing on their higher-dimensional extensions. We also include several interesting examples of algebraic identities obtained form the generalized Ibn al-Haytham formulas and Karaji'sL-summing method. Finally, we will also show the interplay between these two different methodsof summation.

🔖

Cite This Article

Faal, H. T. (2022). Karaji's L-Summing Method and the Generalized Ibn al-Haytham Recursive Formula. Turkish Journal of Mathematics and Computer Science, Cilt: 13 - Sayı: 1, 122–128. https://ajindex.com/articles/609081

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (7)

  1. Greene, D. H., Knuth, D. E., Mathematics for the Analysis of Algorithms (3rd Edition), Birkhauser, Boston, 1990
  2. Hassani, M., Identities by L-summing method, Int. J. Math. Comput. Sci., 1(2006), 165–172
  3. Katz, V. J., Ideas of calculus in Islam and India, Math. Mag., 68(1995), 163–174
  4. Teimoori, H., A Generalization of Ibn Al-Haytham recursive formula for sums of powers, Turk. J. Math. Comput. Sci., 1(2018), 165–172
  5. Teimoori, H. A Systematic way to prove some classes of integer sequences identities, (in preparation)
  6. Woepcke, F., Extrait du Fakhr, Traite D’algebre par Abou Bekr Mohammed Ben Alhacan Alkarkhi, Reprint of the 1853 original, Hildesheim, 1982
  7. Zeilberger, D., The method of creative telescoping, J. Symbolic Comput., 11(1991), 195–204.