In this paper we demonstrate the existence of a set of polynomials Pi , 1 i n , which are positive semi-definite on an interval [a , b] and satisfy, partially, the conditions of polynomials found in the Lagrange interpolation process. In other words, if a a1 an b is a given finite sequence of real numbers, then Pi (a j ) ij (ij is the Kronecker delta symbol ) ; moreover, the sum of Pi 's is identically 1.
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