Specializations of Generalized Laguerre Polynomials
نویسندگان
چکیده
منابع مشابه
Specializations of Generalized Laguerre Polynomials
Three specializations of a set of orthogonal polynomials with “8 different q’s” are given. The polynomials are identified as q-analogues of Laguerre polynomials, and the combinatorial interpretation of the moments give infinitely many new Mahonian statistics on permutations.
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The second author dedicates this paper to the one and only Dick Askey, his mathematical father. Abstract. Three specializations of a set of orthogonal polynomials with " 8 different q's " are given. The polynomials are identified as q-analogues of Laguerre polynomi-als, and the combinatorial interpretation of the moments give infinitely many new Mahonian statistics on permutations.
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where α + β + 1 > β > 1 −m, σ + 1 > α + β > 0, m is a positive integer, and 0 < h < ∞, 0 ≤ b <∞, and h and b are finite constants. L n [(x + b)h] is a Laguerre polynomial, An are unknown coefficients, and f (x) and g(x) are prescribed functions. Srivastava [5, 6] has solved the following dual series equations: ∞ ∑ n=0 AnL (α) n (x) Γ(α+n+ 1) = f (x), 0 < x < a, (1.3) ∞ ∑ n=0 AnL (σ) n (x) Γ(α+n...
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ژورنال
عنوان ژورنال: SIAM Journal on Mathematical Analysis
سال: 1994
ISSN: 0036-1410,1095-7154
DOI: 10.1137/s003614109322854x