#### Title

Sequences of Numbers Meet the Generalized Gegenbauer-Humbert Polynomials

#### 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.

#### Disciplines

Applied Mathematics | Mathematics

#### Recommended Citation

He, Tian-Xiao; Shiue, Peter; and Weng, Tsui-Wei, "Sequences of Numbers Meet the Generalized Gegenbauer-Humbert Polynomials" (2011). *Scholarship*. 29.

https://digitalcommons.iwu.edu/math_scholarship/29

## Comments

ISRN Discrete Mathematicsis published by Hindawi Publishing Corporation, http://www.hindawi.com/journals/isrn/.