On aq-deformation of the discrete Painlevé I equation andq-orthogonal polynomials
نویسندگان
چکیده
منابع مشابه
On a q-Deformation of the Discrete Painlevé I equation and q-orthogonal Polynomials
I present a q-analog of the discrete Painlevé I equation, and a special realization of it in terms of q-orthogonal polynomials.
متن کاملThe Discrete Painlevé I Hierarchy
The discrete Painlevé I equation (dPI) is an integrable difference equation which has the classical first Painlevé equation (PI) as a continuum limit. dPI is believed to be integrable because it is the discrete isomonodromy condition for an associated (single-valued) linear problem. In this paper, we derive higher-order difference equations as isomonodromy conditions that are associated to the ...
متن کاملOn Discrete Painlevé Equations Associated with the Lattice Kdv Systems and the Painlevé Vi Equation
1 Abstract A new integrable nonautonomous nonlinear ordinary difference equation is presented which can be considered to be a discrete analogue of the Painlevé V equation. Its derivation is based on the similarity reduction on the two-dimensional lattice of integrable partial difference equations of KdV type. The new equation which is referred to as GDP (generalised discrete Painlevé equation) ...
متن کاملOn Discrete Orthogonal Polynomials of Several Variables
Let V be a set of points in R. Define a linear functional L on the space of polynomials, Lf = ∑ x∈V f(x)ρ(x), where ρ is a nonzero function on V . The structure of discrete orthogonal polynomials of several variables with respect to the bilinear form 〈f, g〉 = L(fg) is studied. For a given V , the subspace of polynomials that will generate orthogonal polynomials on V is identified. One result sh...
متن کاملDiscrete entropies of orthogonal polynomials
Let pn, n ∈ N, be the nth orthonormal polynomial on R, whose zeros are λ j , j = 1, . . . , n. Then for each j = 1, . . . , n, ~ Ψj def = ( Ψ1j , . . . ,Ψ 2 nj ) with Ψij = p 2 i−1(λ (n) j ) ( n−1 ∑ k=0 pk(λ (n) j ) ) −1 , i = 1, . . . , n, defines a discrete probability distribution. The Shannon entropy of the sequence {pn} is consequently defined as Sn,j def = − n ∑ i=1 Ψij log ( Ψij ) . In t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Letters in Mathematical Physics
سال: 1994
ISSN: 0377-9017,1573-0530
DOI: 10.1007/bf00751068