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.
| Original language | American English |
|---|---|
| Journal | ISRN Discrete Mathematics |
| Volume | 2011 |
| State | Published - Aug 2011 |
Keywords
- Chebyshev polynomial
- Fibonacci sequence
- Lucas number
- Pell number
- Sequence of order 2
- linear recurrence relation
- the generalized Gegenbauer-Humbert polynomial sequence
Disciplines
- Applied Mathematics
- Mathematics