Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations [PDF]
, 2013 We investigate semi-classical generalizations of the Charlier and Meixner polynomials, which are discrete orthogonal polynomials that satisfy three-term recurrence relations.
Clarkson, Peter
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Parameter Derivatives of the Jacobi Polynomials with Three Variables on the Simplex
MATEC Web of Conferences, 2016 In this paper, an attempt has been made to derive parameter derivatives of Jacobi polynomials with three variables on the simplex. They are obtained via parameter derivatives of the classical Jacobi polynomials Pn(α,β)(x) with respect to their parameters.
Aktaş Rabia
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Jacobi polynomials as generalized Faber polynomials [PDF]
Transactions of the American Mathematical Society, 1990 Let B {\mathbf {B}}
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Zeros of Jacobi and ultraspherical polynomials [PDF]
The Ramanujan Journal, 2021 Suppose $\{P_{n}^{(α, β)}(x)\}_{n=0}^\infty $ is a sequence of Jacobi polynomials with $ α, β>-1.$ We discuss special cases of a question raised by Alan Sokal at OPSFA in 2019, namely, whether the zeros of $ P_{n}^{(α,β)}(x)$ and $ P_{n+k}^{(α+ t, β+ s )}(x)$ are interlacing if $s,t >0$ and $ k \in \mathbb{N}.$ We consider two cases of this ...
Arvesú, J. +2 more
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Properties of the Polynomials Associated with the Jacobi Polynomials [PDF]
Mathematics of Computation, 1986 Power forms and Jacobi polynomial forms are found for the polynomials W n (
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On the Behaviour of Zeros of Jacobi Polynomials
Journal of Approximation Theory, 2002 Denoting by \(x_{n,k}(\alpha,\beta)\) and \(x_{n,k}(\lambda)= x_{n,k} (\lambda-1/2, \lambda-1/2)\) the zeros, in decreasing order, of the Jacobi polynomial \(P_n^{(\alpha,\beta)} (x)\) and of the ultraspherical (or Gegenbauer) polynomial \(C_n^\lambda(x)\), respectively, the authors investigate the monotonicity of \(x_{n,k}(\alpha,\beta)\) as functions
Dimitar K. Dimitrov 0001 +1 more
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New Biparametric Families of Apostol-Frobenius-Euler Polynomials level-m
Математичні Студії, 2021 We introduce two biparametric families of Apostol-Frobenius-Euler polynomials of level-$m$. We give some algebraic properties, as well as some other identities which connect these polynomial class with the generalized $\lambda$-Stirling type numbers of ...
D. Bedoya +3 more
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Large degree asymptotics of orthogonal polynomials with respect to an oscillatory weight on a bounded interval [PDF]
, 2014 We consider polynomials p^w_n(x) that are orthogonal with respect to the oscillatory weight w(x)=exp(iwx) on [?1,1], where w>0 is a real parameter. A first analysis of p^?_n(x) for large values of w was carried out in connection with complex Gaussian ...
Deaño Cabrera, Alfredo, Deaño, Alfredo
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On the Limit from q-Racah Polynomials to Big q-Jacobi Polynomials
Symmetry, Integrability and Geometry: Methods and Applications, 2011 A limit formula from q-Racah polynomials to big q-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials.
Tom H. Koornwinder
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Simplified Expressions of the Multi-Indexed Laguerre and Jacobi Polynomials [PDF]
, 2017 The multi-indexed Laguerre and Jacobi polynomials form a complete set of orthogonal polynomials. They satisfy second-order differential equations but not three term recurrence relations, because of the 'holes' in their degrees. The multi-indexed Laguerre
Sasaki, Ryu +3 more
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