Abstract
The object of this paper is to show that three determinantal identities which appeared in the author's joint paper with Dale [3], and which at the time were thought to be independent, are in fact simple illustrations of a general family of identities. Let M 1 be a persymmetric matrix of modified Appell polynomials ψm(x) and let M 2 be a symmetric matrix of the form where A is a persymmetric array of the constants ψm(0)Pis an array of x-elements with binomial coefficients and O is an array of zeros. Then to each submatrix of M 1 there corresponds a family of distinct submatrices of M 2 the determinants of which represent identical polynomials. The result can be extended to functions of two variables. The paper ends with two determinantal representations of ψm(x) and an identity relating three determinants.
Published Version
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