Yıl: 2016 Cilt: 40 Sayı: 5 Sayfa Aralığı: 960 - 972 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

The generalized reciprocal super Catalan matrix

Öz:
The reciprocal super Catalan matrix studied by Prodinger is further generalized, introducing two additional parameters. Explicit formulae are derived for the LU -decomposition and their inverses, as well as the Cholesky decomposition. The approach is to use q -analysis and to leave the justification of the necessary identities to the q - version of Zeilberger s celebrated algorithm.
Anahtar Kelime:

Konular: Matematik
Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] Andrews GE, Askey R, Roy R. Special Functions. Cambridge, UK: Cambridge University Press, 2000.
  • [2] Carlitz L. The characteristic polynomial of a certain matrix of binomial coefficients. The Fibonacci Quarterly 1965; 3: 81-89.
  • [3] Edelman A, Strang G. Pascal matrices. Am Math Mon 2004; 111: 189-197.
  • [4] Kılı¸c E, Akkus I, Kızılaslan G. A variant of the reciprocal super Catalan matrix. Special Matrices 2015; 3: 163-168.
  • [5] Kılı¸c E, Prodinger H. Variants of the Filbert matrix. The Fibonacci Quarterly 2013; 51: 153-162.
  • [6] Pan VY. Structured Matrices and Polynomials. New York, NY, USA: Springer-Verlag, 2001.
  • [7] Paule P, Riese A. A Mathematica q -analogue of Zeilberger’s algorithm based on an algebraically motivated approach to q -hypergeometric telescoping, in special functions, q -series and related topics, Fields Inst Commun 1997; 14: 179-210.
  • [8] Prodinger H. The reciprocal super Catalan matrix. Special Matrices 2015; 1: 111-117.
  • [9] Petkovsek M, Wilf H, Zeilberger D. ”A = B”. Wellesley, MA, USA: A K Peters, 1996.
  • [10] Richardson TM. The Filbert matrix. The Fibonacci Quarterly 2001; 39: 268-275.
APA Kılıç E, ARIKAN T (2016). The generalized reciprocal super Catalan matrix. , 960 - 972.
Chicago Kılıç Emrah,ARIKAN Talha The generalized reciprocal super Catalan matrix. (2016): 960 - 972.
MLA Kılıç Emrah,ARIKAN Talha The generalized reciprocal super Catalan matrix. , 2016, ss.960 - 972.
AMA Kılıç E,ARIKAN T The generalized reciprocal super Catalan matrix. . 2016; 960 - 972.
Vancouver Kılıç E,ARIKAN T The generalized reciprocal super Catalan matrix. . 2016; 960 - 972.
IEEE Kılıç E,ARIKAN T "The generalized reciprocal super Catalan matrix." , ss.960 - 972, 2016.
ISNAD Kılıç, Emrah - ARIKAN, Talha. "The generalized reciprocal super Catalan matrix". (2016), 960-972.
APA Kılıç E, ARIKAN T (2016). The generalized reciprocal super Catalan matrix. Turkish Journal of Mathematics, 40(5), 960 - 972.
Chicago Kılıç Emrah,ARIKAN Talha The generalized reciprocal super Catalan matrix. Turkish Journal of Mathematics 40, no.5 (2016): 960 - 972.
MLA Kılıç Emrah,ARIKAN Talha The generalized reciprocal super Catalan matrix. Turkish Journal of Mathematics, vol.40, no.5, 2016, ss.960 - 972.
AMA Kılıç E,ARIKAN T The generalized reciprocal super Catalan matrix. Turkish Journal of Mathematics. 2016; 40(5): 960 - 972.
Vancouver Kılıç E,ARIKAN T The generalized reciprocal super Catalan matrix. Turkish Journal of Mathematics. 2016; 40(5): 960 - 972.
IEEE Kılıç E,ARIKAN T "The generalized reciprocal super Catalan matrix." Turkish Journal of Mathematics, 40, ss.960 - 972, 2016.
ISNAD Kılıç, Emrah - ARIKAN, Talha. "The generalized reciprocal super Catalan matrix". Turkish Journal of Mathematics 40/5 (2016), 960-972.