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In this paper, we calculate the generating functions by using the concepts of symmetric functions. Although the methods cited in previous works are in principle constructive, we are concerned here only with the question of manipulating combinatorial objects, known as symmetric op-erators. The proposed generalized symmetric functions can be used to find explicit formulas of the Fibonacci numbers, and of the Tchebychev polynomials of first and second kinds. where σ 1 , σ 2 are called elementarydoi:10.12732/iejpam.v7i4.5 fatcat:6jsvw2gsprhxna3axy4tem37fe