One of the most classical areas of algebra the theory of symmetric functions and orthogonal polynomials has long been known to be connected to combinatorics representation theory and other branches of mathematics. London mathematical society monographs series vol 34 princeton university press symmetric functions and orthogonal polynomials university lecture series vol 12 american mathematical society theory and applications orthogonal polynomials and special functions leuven 2002 lecture notes in mathematics vol 1817 springer . 1 a basic class of symmetric orthogonal polynomials using the extended sturm liouville theorem for symmetric functions mohammad masjed jamei department of mathematics kntoosi university of technology pobox 16315 1618 tehran iran. Abstract a new constructive approach is given to the linearization formulas of symmetric orthogonal polynomials we use the monic three term recurrence relation of an orthogonal polynomial system to set up a partial difference equation problem for the product of two polynomials and solve it in terms of the initial data. 218 symmetric polynomials we obviously want to say that with the constraint that all the symmetric functions of the i being 0 except the last two we have computed the discriminant up to a less interesting constant factor
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