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Sequences Of Numbers Meet The Generalized Gegenbauer-Humbert Polynomials, Tian-Xiao He, Peter J.-S. Shiue, Tsui-Wei Weng
Sequences Of Numbers Meet The Generalized Gegenbauer-Humbert Polynomials, Tian-Xiao He, Peter J.-S. Shiue, Tsui-Wei Weng
Tian-Xiao He
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.
Characterizations Of Orthogonal Generalized Gegenbauer-Humbert Polynomials And Orthogonal Sheffer-Type Polynomials, Tian-Xiao He
Characterizations Of Orthogonal Generalized Gegenbauer-Humbert Polynomials And Orthogonal Sheffer-Type Polynomials, Tian-Xiao He
Tian-Xiao He
We present characterizations of the orthogonal generalized Gegen-bauer-Humbert polynomial sequences and the orthogonal Sheffer-type polynomial sequences. Using a new polynomial sequence transformation technique presented in [12], we give a method to evaluate the measures and their supports of some orthogonal generalized Gegenbauer-Humbert polynomial sequences.