Results 41 to 50 of about 8,973,715 (361)
Multivariate difference Gončarov polynomials
, 2022 17 ...
Adeniran, A., Snider, L., Yan, C.
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, 2020 In this contribution we consider sequences of monic polynomials orthogonal with respect to Sobolev-type inner product \[ \left\langle f,g\right\rangle= \langle {\bf u}^{\tt M},fg\rangle+\lambda \mathscr T^j f (\alpha)\mathscr T^{j}g(\alpha), \] where ...
Costas-Santos, R. S. +2 more
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Plancherel-Rotach Asymptotics of Second-Order Difference Equations with Linear Coefficients [PDF]
, 2014 In this paper, we provide a complete Plancherel-Rotach asymptotic analysis of polynomials that satisfy a second-order difference equation with linear coefficients.
Wang, Xiang-Sheng
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On the Finite Differences of a Polynomial [PDF]
The Annals of Mathematical Statistics, 1935 In this paper an apparently new and convenient method of finding the successive finite differences of a polynomial is considered. If operationally 4(u + rjr2) = Er7r2 4(u) = (1 + Ari)r2 4o(u) then for any polynomial f(x) of degree "n" f(x) = po xn + P, Xn-1 +--+ Pn = po(x + a)n + qll(x + a)n-I + + qln Eaf(x) = po(x + a)n + pl(x + a)n-' + + Pn Aaf(X) = (
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The structure relation for Askey-Wilson polynomials [PDF]
, 2006 An explicit structure relation for Askey-Wilson polynomials is given. This involves a divided q-difference operator which is skew symmetric with respect to the Askey-Wilson inner product and which sends polynomials of degree n to polynomials of degree n ...
Koornwinder, Tom H.
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Polynomial solutions of algebraic difference equations and homogeneous symmetric polynomials
Journal of Symbolic Computation, 2021 This article addresses the problem of computing an upper bound of the degree d of a polynomial solution P(x) of an algebraic difference equation of the form G(x)(P(x−τ1),…,P(x−τs))+G0(x)=0 when such P(x) with the coefficients in a field K of characteristic zero exists and where G is a non-linear s-variable polynomial with coefficients in K[x] and G0 is
Olha Shkaravska +3 more
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Combinatorics and invariant differential operators on multiplicity free spaces [PDF]
, 2003 We study the generalization of shifted Jack polynomials to arbitrary multiplicity free spaces. In a previous paper (math.RT/0006004) we showed that these polynomials are eigenfunctions for commuting difference operators.
Benson +19 more
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A high order $q$-difference equation for $q$-Hahn multiple orthogonal polynomials [PDF]
, 2009 A high order linear $q$-difference equation with polynomial coefficients having $q$-Hahn multiple orthogonal polynomials as eigenfunctions is given. The order of the equation is related to the number of orthogonality conditions that these polynomials ...
Abramowitz M. +10 more
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Unicity of transcendental meromorphic functions concerning differential-difference polynomials
AIMS Mathematics, 2022 Let $ f $ and $ g $ be two transcendental meromorphic functions of finite order with a Borel exceptional value $ \infty $, let $ \alpha $ $ (\not\equiv 0) $ be a small function of both $ f $ and $ g $, let $ d, k, n, m $ and $ v_j (j = 1, 2, \cdots, d) $
Zhiying He, Jianbin Xiao, Mingliang Fang
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, 2016 In this paper, a fourth-order partial divided-difference equation on quadratic lattices with polynomial coefficients satisfied by bivariate Racah polynomials is presented.
Area, I. +4 more
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