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A Generalization of Ibn Al-Haytham Recursive Formula for Sums of Powers

Yıl 2018, Cilt 9, Sayı , 25 - 33, 28.12.2018

Öz

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.

Kaynakça

Abel, N. H. Untersuchungen uber die Reihe $1 + \frac{m}{1} x + \frac{m(m−1)}{1.2}x^{2} + \cdots $ , J. Reine Angew. Math., 1 (1826), 311–339.
Gould, H.W. Table for Fundamentals of Series: Part I, Unpublished Manuscript Notebooks, Edited and Compiled by Jocelyn Quaintance, May 2010.
Graham, R. L., Knuth, D. E., Patashnik, O. Concrete Mathematics: A Foundation for Computer Science, Addison-Wesley Publishing Company, Amsterdam, 2nd Ed., 1994. Hassani, M. Identities by L - summing method, Int. J. Math. Comput. Sci., 1(2006), 165–172.
Katz, V. J., Ideas of calculus in Islam and India, Math. Magazine, 68(1995), 163–174.
Masic, I. , Ibn al-Haytham-father of optics and describer of vision theory, Med Arh, Academy of Medical Sciences of Bosnia and Herzegovina, 62(2008), 183–1880.
Teimoori, H. The generalized Ibn al-Haytham sums of powers formulas and combinatorial identities, In Preparation.
Zeilberger, D. The method of creative telescoping, J. Symbolic Computation, 11(1991), 195–204.

Yıl 2018, Cilt 9, Sayı , 25 - 33, 28.12.2018

Hossein TEİMOORİ FAAL

Öz

Kaynakça

Abel, N. H. Untersuchungen uber die Reihe $1 + \frac{m}{1} x + \frac{m(m−1)}{1.2}x^{2} + \cdots $ , J. Reine Angew. Math., 1 (1826), 311–339.
Gould, H.W. Table for Fundamentals of Series: Part I, Unpublished Manuscript Notebooks, Edited and Compiled by Jocelyn Quaintance, May 2010.
Graham, R. L., Knuth, D. E., Patashnik, O. Concrete Mathematics: A Foundation for Computer Science, Addison-Wesley Publishing Company, Amsterdam, 2nd Ed., 1994. Hassani, M. Identities by L - summing method, Int. J. Math. Comput. Sci., 1(2006), 165–172.
Katz, V. J., Ideas of calculus in Islam and India, Math. Magazine, 68(1995), 163–174.
Masic, I. , Ibn al-Haytham-father of optics and describer of vision theory, Med Arh, Academy of Medical Sciences of Bosnia and Herzegovina, 62(2008), 183–1880.
Teimoori, H. The generalized Ibn al-Haytham sums of powers formulas and combinatorial identities, In Preparation.
Zeilberger, D. The method of creative telescoping, J. Symbolic Computation, 11(1991), 195–204.

Ayrıntılar

Birincil Dil	İngilizce
Bölüm	Makaleler
Yazarlar	Hossein TEİMOORİ FAAL (Sorumlu Yazar) Allameh Tabataba'i University Iran
Yayımlanma Tarihi	28 Aralık 2018
Yayınlandığı Sayı	Yıl 2018, Cilt 9, Sayı

Kaynak Göster

Bibtex	@araştırma makalesi { tjmcs422310, journal = {Turkish Journal of Mathematics and Computer Science}, issn = {}, eissn = {2148-1830}, address = {}, publisher = {Matematikçiler Derneği}, year = {2018}, volume = {9}, pages = {25 - 33}, doi = {}, title = {A Generalization of Ibn Al-Haytham Recursive Formula for Sums of Powers}, key = {cite}, author = {Teimoori Faal, Hossein} }
APA	Teimoori Faal, H. (2018). A Generalization of Ibn Al-Haytham Recursive Formula for Sums of Powers . Turkish Journal of Mathematics and Computer Science , 9 , 25-33 . Retrieved from https://dergipark.org.tr/tr/pub/tjmcs/issue/42016/422310
MLA	Teimoori Faal, H. "A Generalization of Ibn Al-Haytham Recursive Formula for Sums of Powers" . Turkish Journal of Mathematics and Computer Science 9 (2018 ): 25-33 <https://dergipark.org.tr/tr/pub/tjmcs/issue/42016/422310>
Chicago	Teimoori Faal, H. "A Generalization of Ibn Al-Haytham Recursive Formula for Sums of Powers". Turkish Journal of Mathematics and Computer Science 9 (2018 ): 25-33
RIS	TY - JOUR T1 - A Generalization of Ibn Al-Haytham Recursive Formula for Sums of Powers AU - Hossein Teimoori Faal Y1 - 2018 PY - 2018 N1 - DO - T2 - Turkish Journal of Mathematics and Computer Science JF - Journal JO - JOR SP - 25 EP - 33 VL - 9 IS - SN - -2148-1830 M3 - UR - Y2 - 2018 ER -
EndNote	%0 Turkish Journal of Mathematics and Computer Science A Generalization of Ibn Al-Haytham Recursive Formula for Sums of Powers %A Hossein Teimoori Faal %T A Generalization of Ibn Al-Haytham Recursive Formula for Sums of Powers %D 2018 %J Turkish Journal of Mathematics and Computer Science %P -2148-1830 %V 9 %N %R %U
ISNAD	Teimoori Faal, Hossein . "A Generalization of Ibn Al-Haytham Recursive Formula for Sums of Powers". Turkish Journal of Mathematics and Computer Science 9 / (Aralık 2018): 25-33 .
AMA	Teimoori Faal H. A Generalization of Ibn Al-Haytham Recursive Formula for Sums of Powers. TJMCS. 2018; 9: 25-33.
Vancouver	Teimoori Faal H. A Generalization of Ibn Al-Haytham Recursive Formula for Sums of Powers. Turkish Journal of Mathematics and Computer Science. 2018; 9: 25-33.
IEEE	H. Teimoori Faal , "A Generalization of Ibn Al-Haytham Recursive Formula for Sums of Powers", Turkish Journal of Mathematics and Computer Science, c. 9, ss. 25-33, Ara. 2018