Abstract. The aim of this paper is to present two fundamental applications of the, so called, Prodinger's algebraic identities. On the one hand we will receive the wide class of trigonometric identities, including identities for Chebyshev polynomials of the first and second kinds. On the second hand we will present the generalizations for Fibonacci and Lucas polynomials of some identities, proved by Prodinger for Fibonacci and Lucas numbers.

Received: June 4, 2010

AMS Subject Classification: 12D05, 11B39, 11B83

Key Words and Phrases: Prodinger's identities, Kummer identities, Chebyshev polynomials, Fibonacci polynomials, Lucas polynomials

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 64
Issue: 2