Sequences of Numbers Meet the Generalized Gegenbauer-Humbert Polynomials. (26th October 2011) - He, Tian-Xiao; Shiue, Peter J.-S.; Weng, Tsui-Wei
Abstract : 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.