Evaluation of sums involving products of Gaussian qq-binomial coefficients with applications to Fibonomial sums

PRODINGER, Helmut; Kılıç, Emrah

Evaluation of sums involving products of Gaussian qq-binomial coefficients with applications to Fibonomial sums

Emrah KILIÇ, (TOBB Ekonomi ve Teknoloji Üniversitesi, Matematik Bölümü, Ankara, Türkiye)

Helmut PRODINGER (Department of Mathematics, University of Stellenbosch, Stellenbosch, South Africa)

Turkish Journal of Mathematics

3 0

Yıl: 2017 Cilt: 41 Sayı: 3 Sayfa Aralığı: 707 - 719 Metin Dili: Diğer İndeks Tarihi: 29-07-2022

Evaluation of sums involving products of Gaussian qq-binomial coefficients with applications to Fibonomial sums

Öz:

Anahtar Kelime:

Konular: Matematik

Öz:

Sums of products of two Gaussian q -binomial coefficients with a parametric rational weight function are considered. The partial fraction decomposition technique is used to evaluate the sums in closed form. Interesting applications of these results to certain generalized Fibonomial and Lucanomial sums are provided.

Anahtar Kelime:

Konular: Matematik

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Horadam AF. Generating functions for powers of a certain generalized sequence of numbers. Duke Math J 1965; 32: 437-446.
[2] Kılı¸c E. The generalized Fibonomial matrix. European J Comb 2008; 29: 701-711.
[3] Kılı¸c E, Prodinger H. Evaluation of sums involving Gaussian q -binomial coefficients with rational weight functions. Inter J Number Theory 2016; 12: 495-504.
[4] Kılı¸c E, Prodinger H. Formulæ related to the q -Dixon formula with applications to Fibonomial sums. Period Math Hung 2015; 70: 216-226.
[5] Kılı¸c E, Prodinger H. Closed form evaluation of sums containing squares of Fibonomial coefficients. Math Slovaca 2016; 66: 757.
[6] Marques D, Trojovsky P. On some new sums of Fibonomial coefficients. The Fibonacci Quarterly 2012; 50: 155-162.
[7] Seibert J, Trojovsky P. On some identities for the Fibonomial coefficients. Math Slovaca 2005; 55: 9-19.
[8] Trojovsky P. On some identities for the Fibonomial coefficients via generating function. Discrete Appl Math 2007; 155: 2017-2024.

APA	Kılıç E, PRODINGER H (2017). Evaluation of sums involving products of Gaussian qq-binomial coefficients with applications to Fibonomial sums. , 707 - 719.
Chicago	Kılıç Emrah,PRODINGER Helmut Evaluation of sums involving products of Gaussian qq-binomial coefficients with applications to Fibonomial sums. (2017): 707 - 719.
MLA	Kılıç Emrah,PRODINGER Helmut Evaluation of sums involving products of Gaussian qq-binomial coefficients with applications to Fibonomial sums. , 2017, ss.707 - 719.
AMA	Kılıç E,PRODINGER H Evaluation of sums involving products of Gaussian qq-binomial coefficients with applications to Fibonomial sums. . 2017; 707 - 719.
Vancouver	Kılıç E,PRODINGER H Evaluation of sums involving products of Gaussian qq-binomial coefficients with applications to Fibonomial sums. . 2017; 707 - 719.
IEEE	Kılıç E,PRODINGER H "Evaluation of sums involving products of Gaussian qq-binomial coefficients with applications to Fibonomial sums." , ss.707 - 719, 2017.
ISNAD	Kılıç, Emrah - PRODINGER, Helmut. "Evaluation of sums involving products of Gaussian qq-binomial coefficients with applications to Fibonomial sums". (2017), 707-719.

APA	Kılıç E, PRODINGER H (2017). Evaluation of sums involving products of Gaussian qq-binomial coefficients with applications to Fibonomial sums. Turkish Journal of Mathematics, 41(3), 707 - 719.
Chicago	Kılıç Emrah,PRODINGER Helmut Evaluation of sums involving products of Gaussian qq-binomial coefficients with applications to Fibonomial sums. Turkish Journal of Mathematics 41, no.3 (2017): 707 - 719.
MLA	Kılıç Emrah,PRODINGER Helmut Evaluation of sums involving products of Gaussian qq-binomial coefficients with applications to Fibonomial sums. Turkish Journal of Mathematics, vol.41, no.3, 2017, ss.707 - 719.
AMA	Kılıç E,PRODINGER H Evaluation of sums involving products of Gaussian qq-binomial coefficients with applications to Fibonomial sums. Turkish Journal of Mathematics. 2017; 41(3): 707 - 719.
Vancouver	Kılıç E,PRODINGER H Evaluation of sums involving products of Gaussian qq-binomial coefficients with applications to Fibonomial sums. Turkish Journal of Mathematics. 2017; 41(3): 707 - 719.
IEEE	Kılıç E,PRODINGER H "Evaluation of sums involving products of Gaussian qq-binomial coefficients with applications to Fibonomial sums." Turkish Journal of Mathematics, 41, ss.707 - 719, 2017.
ISNAD	Kılıç, Emrah - PRODINGER, Helmut. "Evaluation of sums involving products of Gaussian qq-binomial coefficients with applications to Fibonomial sums". Turkish Journal of Mathematics 41/3 (2017), 707-719.