منابع مشابه
Some bilinear generating functions.
In the present paper, the author applies some of his earlier results which extend the well-known Hille-Hardy formula for the Laguerre polynomials to certain classes of generalized hypergeometric polynomials in order to derive various generalizations of a bilinear generating function for the Jacobi polynomials proved recently by Carlitz. The corresponding results for the polynomials of Legendre,...
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Let a1, a2, . . . , an be distinct, positive integers with (a1, a2, . . . , an) = 1, and let k be an arbitrary field. Let H(a1, . . . , an; z) denote the Hilbert series of the graded algebra k[ta1 , ta2 , . . . , tan ]. We show that, when n = 3, this rational function has a simple expression in terms of a1, a2, a3; in particular, the numerator has at most six terms. By way of contrast, it is kn...
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Let V be an infinite matrix with rows and columns indexed by the positive integers, and entries in a field F . Suppose that vi,j only depends on i − j and is 0 for |i − j| large. Then V n is defined for all n, and one has a “generating function” G = ∑ a1,1(V )z. Ira Gessel has shown that G is algebraic over F (z). We extend his result, allowing vi,j for fixed i − j to be eventually periodic in ...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 1963
ISSN: 0012-7094
DOI: 10.1215/s0012-7094-63-03021-7