Öz
Kaynakça
- [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.
Öz
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.
Anahtar Kelimeler
Karaji the generalized Ibn al-Haytham formula summation techniques sums of powers harmonic numbers
Kaynakça
- [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.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Haziran 2021 |
| Yayımlandığı Sayı | Yıl 2021 Cilt: 13 Sayı: 1 |