Sequences of Non-Gegenbauer-Humbert Polynomials Meet the Generalized Gegenbauer-Humbert Polynomials. (30th June 2011) - He, Tian-Xiao; Shiue, Peter J.-S.
Abstract : 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.