Recurrence relations for polynomial sequences via Riordan matrices. (English) Zbl 1250.11029

Luzón, Ana; Morón, Manuel A.

Linear Algebra Appl. 433, No. 7, 1422-1446 (2010).

Summary: 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.

MSC:

11B83	Special sequences and polynomials
33C65	Appell, Horn and Lauricella functions
68W30	Symbolic computation and algebraic computation
68R05	Combinatorics in computer science
05A40	Umbral calculus
05E15	Combinatorial aspects of groups and algebras (MSC2010)

Keywords:

recurrence relation; Riordan matrix; generalized Appell polynomial; polynomial sequence of Riordan type; umbral calculus

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