Recurrence relations for polynomial sequences via Riordan matrices

Linear Algebra and Its Applications

Volumn 433, Issue 7, 2010, Pages 1422-1446

  Luzón, Ana ^a   Morón, Manuel A ^b  

^a UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

^b UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

Generalized Appell polynomial; Polynomial sequence of riordan type; Recurrence relation; Riordan matrix; Umbral calculus

Indexed keywords

APPELL POLYNOMIALS; GENERALIZED APPELL POLYNOMIAL; MATRIX; RECURRENCE RELATIONS; UMBRAL CALCULUS;

CALCULATIONS; MATRIX ALGEBRA;

POLYNOMIALS;

EID: 77955553735     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2010.05.021     Document Type: Article

References (18)

1. 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
2. R.P. Boas, and R.C. Buck Polynomial Expansions of Analytic Functions 1964 Springer-Verlag
3. K. Boubaker, A. Chaouachi, M. Amlouk, and H. Bouzouita Enhancement of pyrolysis spray disposal perfomance using thermal time-response to precursor uniform deposition Eur. Phys. J. Appl. Phys. 37 2007 105 109
4. T.-X. He, L.C. Hsu, and P.J.-S. Shiue The Sheffer group and the Riordan group Discrete Appl. Math. 155 2007 1895 1909
5. I.C. Huang Inverse relations and Schauder bases J. Combin. Theory Ser. A 97 2002 203 224
6. D.E. Knuth Convolution polynomials Math. J. 2 1992 67 78
7. H. Labiadh, M. Dada, B. Awojoyogbe, B. Mahmoud, and 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. n°1 2008 52 66
8. A. Luzón, Iterative processes related to Riordan arrays: the reciprocation and the inversion of power series, preprint.
9. A. Luzón, and M.A. Morón Ultrametrics, Banach's fixed point theorem and the Riordan group Discrete Appl. Math. 156 2008 2620 2635
10. A. Luzón, and M.A. Morón Riordan matrices in the reciprocation of quadratic polynomials Linear Algebra Appl. 430 2009 2254 2270
11. D. Merlini, D.G. Rogers, R. Sprugnoli, and M.C. Verri On some alternative characterizations of Riordan arrays Canad. J. Math. 49 2 1997 301 320
12. D.G. Rogers Pascal triangles, Catalan numbers and renewal arrays Discrete Math. 22 1978 301 310
13. Steven Roman The Umbral Calculus 1984 Academic Press Inc
14. S. Roman, and G.-C. Rota The umbral calculus Adv. Math. 27 1978 95 188
15. G.C. Rota, D. Kahaner, and A. Odlyzko On the fundations of combinatorial theory, VIII: Finite operators calculus J. Math. Anal. Appl. 42 1973 684 760
16. L.W. Shapiro, S. Getu, W.J. Woan, and L. Woodson The Riordan group Discrete Appl. Math. 34 1991 229 239
17. R. Sprugnoli Riordan arrays and combinatorial sums Discrete Math. 132 1994 267 290
18. W. Wang, and T. Wang Generalized Riordan arrays Discrete Math. 308 2008 6466 6500