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Year 2021, , 122 - 128, 30.06.2021
https://doi.org/10.47000/tjmcs.717074

Abstract

References

  • [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.

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

Year 2021, , 122 - 128, 30.06.2021
https://doi.org/10.47000/tjmcs.717074

Abstract

In this paper, we first review two folkloric summation techniques
due 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's
L-summing method. Finally, we
will also show the interplay between these two different methods
of summation.

References

  • [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.
There are 7 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Hossein Teimoori Faal 0000-0001-5861-6287

Publication Date June 30, 2021
Published in Issue Year 2021

Cite

APA Teimoori Faal, H. (2021). Karaji’s L-Summing Method and the Generalized Ibn al-Haytham Recursive Formula. Turkish Journal of Mathematics and Computer Science, 13(1), 122-128. https://doi.org/10.47000/tjmcs.717074
AMA Teimoori Faal H. Karaji’s L-Summing Method and the Generalized Ibn al-Haytham Recursive Formula. TJMCS. June 2021;13(1):122-128. doi:10.47000/tjmcs.717074
Chicago Teimoori Faal, Hossein. “Karaji’s L-Summing Method and the Generalized Ibn Al-Haytham Recursive Formula”. Turkish Journal of Mathematics and Computer Science 13, no. 1 (June 2021): 122-28. https://doi.org/10.47000/tjmcs.717074.
EndNote Teimoori Faal H (June 1, 2021) Karaji’s L-Summing Method and the Generalized Ibn al-Haytham Recursive Formula. Turkish Journal of Mathematics and Computer Science 13 1 122–128.
IEEE H. Teimoori Faal, “Karaji’s L-Summing Method and the Generalized Ibn al-Haytham Recursive Formula”, TJMCS, vol. 13, no. 1, pp. 122–128, 2021, doi: 10.47000/tjmcs.717074.
ISNAD Teimoori Faal, Hossein. “Karaji’s L-Summing Method and the Generalized Ibn Al-Haytham Recursive Formula”. Turkish Journal of Mathematics and Computer Science 13/1 (June 2021), 122-128. https://doi.org/10.47000/tjmcs.717074.
JAMA Teimoori Faal H. Karaji’s L-Summing Method and the Generalized Ibn al-Haytham Recursive Formula. TJMCS. 2021;13:122–128.
MLA Teimoori Faal, Hossein. “Karaji’s L-Summing Method and the Generalized Ibn Al-Haytham Recursive Formula”. Turkish Journal of Mathematics and Computer Science, vol. 13, no. 1, 2021, pp. 122-8, doi:10.47000/tjmcs.717074.
Vancouver Teimoori Faal H. Karaji’s L-Summing Method and the Generalized Ibn al-Haytham Recursive Formula. TJMCS. 2021;13(1):122-8.