Biorthogonal polynomial systems associate with Hermitepolynomials and 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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In this paper, a new and ecient approach based on operational matrices with respect to the gener-alized Laguerre polynomials for numerical approximation of the linear ordinary dierential equations(ODEs) with variable coecients is introduced. Explicit formulae which express the generalized La-guerre expansion coecients for the moments of the derivatives of any dierentiable function in termsof th...
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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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belong to one of the three family of orthogonal polynomials, the other two being Jacobi and Legendre. In addition to their important roles in mathematical analysis, these polynomials also feature prominently in algebra and number theory. Schur ([7], [8]) pioneered the study of Galois properties of specializations of these orthogonal polynomials, and Feit [1] used them to solve the inverse Galoi...
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ژورنال
عنوان ژورنال: SCIENTIA SINICA Mathematica
سال: 2020
ISSN: 1674-7216
DOI: 10.1360/ssm-2020-0074