Open AccessSequences of Numbers Meet the Generalized Gegenbauer-Humbert Polynomials
Author(s) -
Tian-Xiao He,
Peter J.-S. Shiue,
Tsui-Wei Weng
Publication year - 2011
Publication title -
isrn discrete mathematics
Language(s) - English
Resource type - Journals
ISSN - 2090-7788
DOI - 10.5402/2011/674167
Subject(s) - lucas number , fibonacci polynomials , mathematics , recurrence relation , fibonacci number , gegenbauer polynomials , lucas sequence , sequence (biology) , classical orthogonal polynomials , discrete orthogonal polynomials , wilson polynomials , combinatorics , polynomial , difference polynomials , orthogonal polynomials , algebra over a field , discrete mathematics , pure mathematics , mathematical analysis , biology , genetics
Here we present a connection between a sequence of numbers generated by a linear recurrence relation of order 2 and sequences of the generalized Gegenbauer-Humbert polynomials. Many new and known formulas of the Fibonacci, the Lucas, the Pell, and the Jacobsthal numbers in terms of the generalized Gegenbauer-Humbert polynomial values are given. The applications of the relationship to the construction of identities of number and polynomial value sequences defined by linear recurrence relations are also discussed.
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