Sequences of non-Gegenbauer-Humbert polynomials meet the generalized Gegenbauer-Humbert polynomials
type: Item
instance of: scholarly article
title: Sequences of non-Gegenbauer-Humbert polynomials meet the generalized Gegenbauer-Humbert polynomials
zbMATH Open document ID: 1221.33030
DOI: 10.5402/2011/268096
author: Tian-Xiao He
author: Peter J.-S. Shiue
published in: ISRN Algebra
publication date: 2011-07-22T00:00:00Z
review text: Summary: Here, we present a connection between a sequence of polynomials generated by a linear recurrence relation of order 2 and sequences of the generalized Gegenbauer-Humbert polynomials. Many new and known transfer formulas between non-Gegenbauer-Humbert polynomials and generalized Gegenbauer-Humbert polynomials are given. The applications of the relationship to the construction of identities of polynomial sequences defined by linear recurrence relations are also discussed.
Mathematics Subject Classification ID: 33D45
zbMATH DE Number: 5931116
zbMATH Keywords: transfer formulas
zbMATH Keywords: linear recurrence
Wikidata QID: Q58689146
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.5402/2011/268096
OpenAlex ID: W2148885192
cites work: Q4064230
cites work: Q3340980
cites work: Towards computerized proofs of identities
cites work: On sequences of numbers and polynomials defined by linear recurrence relations of order 2
cites work: Fibonacci, Chebyshev, and Orthogonal Polynomials
cites work: Five-Diagonal Toeplitz Determinants an Their Relation to Chebyshev Polynomials
cites work: Sequences of numbers meet the generalized Gegenbauer-Humbert polynomials
cites work: Inverse series relations and other expansions involving Humbert polynomials
cites work: A symbolic operator approach to several summation formulas for power series. II
cites work: Fibonacci and Lucas numbers with applications. Volume I
cites work: Q4325515
cites work: Q4281099
cites work: Cycle indicators and special functions
cites work: Q3222256
cites work: Q3852264
cites work: Q4791752
cites work: Q3997537
cites work: Q5589310
cites work: Inverse Relations and Combinatorial Identities
cites work: Forbidden subsequences and Chebyshev polynomials
cites work: Q4222737
Recommended article: Sequences of numbers meet the generalized Gegenbauer-Humbert polynomials
Recommended article: Q4528606
Recommended article: Generalized Humbert polynomials via generalized Fibonacci polynomials
Recommended article: On sequences of Hurwitz polynomials related to orthogonal polynomials
Recommended article: On a generalization of the generating function for Gegenbauer polynomials
Recommended article: Generalizations on Humbert polynomials and functions
Recommended article: Q3756546
Recommended article: Q5399760
Recommended article: A class of Laguerre-based generalized Humbert polynomials
description: scientific article; zbMATH DE number 5931116