Abstract
The matrices of order n defined, in terms of the n arbitrary numbers x j , by the formulae X= diag(x j) and Z jk=δ jk ∑′ l=1 n (x j−x l) −1+(1−δ jk(x j−x k) −1 , are representations of the multiplicative operator ξ and of the differential operator d/ dξ in a space spanned by the polynomials in ξ of degree less than n. This elementary fact implies a number of remarkable formulae involving these matrices, including novel representations of the classical polynomials.
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