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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The object of the present paper is to investigate several general families of bilinear and bilateral generating functions with different argument for the Gauss’ hypergeometric polynomials. Mathematics Subject Classification(2010): Primary 42C05, Secondary 33C45. Keywords—Appell’s functions, Gauss hypergeometric functions, Heat polynomials, Kampe’ de Fe’riet function, Laguerre polynomials, Lauri...
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In this work we study numbers and polynomials generated by two type of composition of generating functions and get their explicit formulae. Furthermore we state an improvementof the composita formulae's given in [6] and [3], using the new composita formula's we construct a variety of combinatorics identities. This study go alone to dene new family of generalized Bernoulli polynomials which incl...
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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...
متن کاملGenerating Functions Attached to some Infinite Matrices
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: Proceedings of the National Academy of Sciences
سال: 1969
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.64.2.462