Complete symmetric functions and generating functions

Abstract

In this paper we propose an alternative approach for the determination of the Fibonacci numbers and some results of Foata, Ramanujan and other results on Chebychev polynomials of first and second kinds. This approach is based on the action of the symmetrizes endomorphism operators Ï€_{eâ‚eâ‚‚}^{k+1} on the sequences ∑_{n=0}^{+∞}S_{n}(A)zâ¿. Satisfactory results were obtained in almost all of the treated cases. Moreover, we give new results for the Stirling numbers.