Complete symmetric functions and generating functions

  • Ali Boussayoud LMAM Laboratory and Department of Mathematics, Mohamed Seddik Ben Yahia University, Jijel, Algeria


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 π_{e₁e₂}^{k+1} on the sequences ∑_{n=0}^{+∞}S_{n}(A)zⁿ. Satisfactory results were obtained in almost all of the treated cases. Moreover, we give new results for the Stirling numbers.