Alonso Morón , Manuel and Luzón, Ana (2010) Recurrence relations for polynomial sequences via Riordan matrices. Linear Algebra and its Applications, 433 (7). pp. 1422-1446. ISSN 0024-3795
Restricted to Repository staff only until 31 December 2020.
We give recurrence relations for any family of generalized Appell polynomials unifying so some known recurrences for many classical sequences of polynomials. Our main tool to get our goal is the Riordan group. We use the product of Riordan matrices to interpret some relationships between different polynomial families. Moreover using the Hadamard product of series we get a general recurrence relation for the polynomial sequences associated to the so called generalized umbral calculus.
|Uncontrolled Keywords:||Arrays; calculus; recurrence relation; Riordan matrix; generalized Appell polynomial; polynomial sequence of Riordan type; umbral calculus|
|Subjects:||Sciences > Mathematics > Algebra|
 E.T. Bell, The history of Blissard’s symbolic method, with a sketch of its inventor’s life, Amer. Math. Monthly 45 (7) (1938) 414–421.
 R.P. Boas, R.C. Buck, Polynomial Expansions of Analytic Functions, Springer-Verlag, 1964.
 K. Boubaker, A. Chaouachi, M. Amlouk, H. Bouzouita, Enhancement of pyrolysis spray disposal performance using thermal time-response to precursor uniform deposition, Eur. Phys. J. Appl. Phys. 37 (2007) 105–109.
 T.-X. He, L.C. Hsu, P.J.-S. Shiue, The Sheffer group and the Riordan group, Discrete Appl. Math. 155 (2007) 1895–1909.
 I.C. Huang, Inverse relations and Schauder bases, J. Combin. Theory Ser. A 97 (2002) 203–224.
 D.E. Knuth, Convolution polynomials, Math. J. 2 (1992) 67–78.
 H. Labiadh, M. Dada, B. Awojoyogbe, B. Mahmoud, A. Bannour, Establishment of an ordinary generating function and a Christoffel–Darboux type first-order differential equation for the heat equation related Boubaker–Turki polynomials, Differential Equations Control Process. (no. 1) (2008) 52–66.
 A. Luzón, Iterative processes related to Riordan arrays: the reciprocation and the inversion of power series, preprint.
 A. Luzón, M.A. Morón, Ultrametrics, Banach’s fixed point theorem and the Riordan group, Discrete Appl. Math. 156 (2008) 2620–2635.
 A. Luzón, M.A. Morón, Riordan matrices in the reciprocation of quadratic polynomials, Linear Algebra Appl. 430 (2009) 2254–2270.
 D. Merlini, D.G. Rogers, R. Sprugnoli, M.C. Verri, On some alternative characterizations of Riordan arrays, Canad. J. Math. 49 (2) (1997) 301–320.
 D.G. Rogers, Pascal triangles, Catalan numbers and renewal arrays, Discrete Math. 22 (1978) 301–310.
 Steven Roman, The Umbral Calculus, Academic Press Inc, 1984.
 S. Roman, G.-C. Rota, The umbral calculus, Adv. Math. 27 (1978) 95–188.
 G.C. Rota, D. Kahaner, A. Odlyzko, On the foundations of combinatorial theory, VIII: Finite operators calculus, J. Math. Anal. Appl. 42 (1973) 684–760.
 L.W. Shapiro, S. Getu,W.J.Woan, L.Woodson, The Riordan group, Discrete Appl. Math. 34 (1991) 229–239.
 R. Sprugnoli, Riordan arrays and combinatorial sums, Discrete Math. 132 (1994) 267–290.
 W.Wang, T.Wang, Generalized Riordan arrays, Discrete Math. 308 (2008) 6466–6500.
|Deposited On:||24 Apr 2012 12:10|
|Last Modified:||24 Apr 2012 12:10|
Repository Staff Only: item control page