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A variant of the reciprocal super Catalan matrix

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Recently Prodinger [8] considered the reciprocal super Catalan matrix and gave explicit formulæ for its LU-decomposition, the LU-decomposition of its inverse, and obtained some related matrices. For all results, q-analogues were also presented. In this paper, we define and study a variant of the reciprocal super Catalan matrix with two additional parameters. Explicit formulæ for its LU-decomposition, LUdecomposition of its inverse and the Cholesky decomposition are obtained. For all results, q-analogues are also presented.
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
1
Opis fizyczny
Daty
otrzymano
2015-06-23
zaakceptowano
2015-07-12
online
2015-07-27
Twórcy
  • TOBB University of Economics and Technology, Mathematics Department, 06560 Ankara Turkey
autor
  • Kırıkkale University, Faculty of Science and Arts, Department of Mathematics, 71450 Kırıkkale Turkey
  • Kırıkkale University, Faculty of Science and Arts, Department of Mathematics, 71450 Kırıkkale Turkey
Bibliografia
  • [1] J. E. Andersen and C. Berg, Quantum Hilbert matrices and orthogonal polynomials, math.CA:arXiv:math/0703546v1.
  • [2] M. D. Choi, Tricks or treats with the Hilbert matrix, Amer. Math. Monthly 90 (5) (1983), 301–312.
  • [3] D. Hilbert, Ein Beitrag zur Theorie des Legendreschen Polynoms, Acta Math. 18 (1894), 155–159. (367–370 in “GesammelteAbhandlungen II”, Berlin 1933.)[Crossref]
  • [4] E. Kılıç and H. Prodinger, The q-Pilbert matrix, Inter. J. Computer Math., 89 (10) (2012), 1370–1377.
  • [5] E. Kılıç and H. Prodinger, Variants of the Filbert matrix, The Fibonacci Quarterly 51(2) (2013), 153–162.
  • [6] V. Y. Pan, Structured matrices and polynomials, Birkhauser Boston, Inc., Boston, MA, Springer-Verlag, New York, 2001.
  • [7] M. Petkovsek, H. Wilf, and D. Zeilberger, A = B, A.K. Peters, Ltd., 1996.
  • [8] H. Prodinger, The reciprocal super Catalan matrix, Special Matrices 3 (2015), 111–117
  • [9] T. M. Richardson, The Filbert matrix, The Fibonacci Quarterly 39 (3) (2001), 268–275.
  • [10] T. M. Richardson. The reciprocal Pascal matrix, ArXiv:1405.6315, 2014.
  • [11] A. Riese, A Mathematica q-analogue of Zeilberger’s algorithm for proving q-hypergeometric identities, Diploma Thesis,RISC, J. Kepler University, Linz, Austria, 1995.
  • [12] A. Riese, http://www.risc.uni-linz.ac.at/research/combinat/software/qZeil/index.php.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_spma-2015-0014
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