Sequences of Numbers Meet the Generalized Gegenbauer-Humbert Polynomials
Copyright policy )Sequences of Numbers Meet the Generalized Gegenbauer-Humbert Polynomials
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.
- University of Nevada, Las Vegas United States
- National Taiwan University of Arts Taiwan
- Illinois Wesleyan University United States
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Fibonacci and Lucas numbers and polynomials and generalizations, Recurrences, Other special orthogonal polynomials and functions
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Fibonacci and Lucas numbers and polynomials and generalizations, Recurrences, Other special orthogonal polynomials and functions
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