L-classical d-orthogonal polynomial sets of Sheffer type
نویسندگان
چکیده
منابع مشابه
Linearization coefficients for Sheffer polynomial sets via lowering operators
The lowering operator σ associated with a polynomial set {P n } n≥0 is an operator not depending on n and satisfying the relation σP n = nP n−1. In this paper, we express explicitly the linearization coefficients for polynomial sets of Sheffer type using the corresponding lowering operators. We obtain some well-known results as particular cases.
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1 Gruppo Fisica Teorica e Matematica Applicata, Unità Tecnico Scientifica Tecnologie Fisiche Avanzate, ENEA-Centro Ricerche Frascati, C.P. 65, Via Enrico Fermi 45, 00044 Frascati, Rome, Italy 2 Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate, Sapienza Università di Roma, Via A. Scarpa 14, 00161 Roma, Italy 3 International Telematic University Uninettuno, Corso Vittorio Eman...
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Here we present a characterization of Sheffer-type polynomial sequences based on the isomorphism between the Riordan group and Sheffer group and the sequence characterization of Riordan arrays. We also give several alternative forms of the characterization of the Riordan group, Sheffer group and their subgroups. Formulas for the computation of the generating functions of Riordan arrays and Shef...
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Riordan group concepts are combined with the basic properties of convolution families of polynomials and Sheffer sequences, to establish a duality law, canonical forms ρ(n,m) = ( n m ) cFn−m(m), c 6= 0, and extensions ρ(x, x − k) = (−1) xcFk(x), where the Fk(x) are polynomials in x, holding for each ρ(n,m) in a Riordan array. Examples ρ(n,m) = ( n m ) Sk(x) are given, in which the Sk(x) are “or...
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Following the approach of Rota and Taylor [17], we present an innovative theory of Sheffer sequences in which the main properties are encoded by using umbrae. This syntax allows us noteworthy computational simplifications and conceptual clarifications in many results involving Sheffer sequences. To give an indication of the effectiveness of the theory, we describe applications to the well-known...
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ژورنال
عنوان ژورنال: Filomat
سال: 2019
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil1903881c