Warianty tytułu
Języki publikacji
Abstrakty
In this second article on q-Pascal matrices, we show how the previous factorizations by the summation matrices and the so-called q-unit matrices extend in a natural way to produce q-analogues of Pascal matrices of two variables by Z. Zhang and M. Liu as follows [...] We also find two different matrix products for [...]
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Numer
Opis fizyczny
Daty
otrzymano
2015-07-15
zaakceptowano
2015-09-14
online
2015-10-06
Twórcy
autor
- Department of Mathematics, Uppsala University, P.O. Box 480, SE-751 06 Uppsala, Sweden
Bibliografia
- [1] W. A. Al-Salam, q-Bernoulli numbers and polynomials, Math. Nachr 17 (1959), 239–260.[Crossref]
- [2] R. Brawer and M. Pirovino, The linear algebra of the Pascal matrix, Linear Algebra Appl. 174 (1992), 13–23.
- [3] T. Ernst, q-Leibniz functional matrices with applications to q-Pascal and q-Stirling matrices, Adv. Stud. Contemp. Math.,Kyungshang 22 (2012), 537-555.
- [4] T. Ernst, q-Pascal and q-Wronskian matrices with implications to q-Appell polynomials, J. Discrete Math., (2013), Article ID450481, 10 p.
- [5] T. Ernst, A comprehensive treatment of q-calculus, Birkhäuser 2012.
- [6] T. Ernst, An umbral approach to find q-analogues of matrix formulas, Linear Algebra Appl. 439 (2013), 1167–1182.[WoS]
- [7] T. Ernst, Faktorisierungen von q-Pascalmatrizen (Factorizations of q-Pascal matrices), Algebras Groups Geom. 31 (2014),no. 4, 387-405
- [8] H. Exton, q-Hypergeometric functions and applications, Ellis Horwood 1983.
- [9] F.H. Jackson, A basic-sine and cosine with symbolical solution of certain differential equations, Proc. EdinburghMath. Soc.22 (1904), 28–39.
- [10] P. Nalli, On a calculation procedure similar to integration, (Sopra un procedimento di calcolo analogo all integrazione)(Italian), Palermo Rend 47 (1923), 337–374.
- [11] M. Ward, A calculus of sequences, Amer. J. Math. 58 (1936), 255–266.
- [12] Z. Zhang, The linear algebra of the generalized Pascal matrix, Linear Algebra Appl. 250 (1997), 51–60.
- [13] Z. Zhang and M. Liu, An extension of the generalized Pascal matrix and its algebraic properties, Linear Algebra Appl. 271(1998), 169–177.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_spma-2015-0020