相关论文: Special polynomials associated with the K2 hierarc…
Differential equations for the special polynomials associated with the rational solutions of the second Painleve hierarchy are introduced. It is shown rational solutions of the Korteveg - de Vries hierarchy can be found taking the…
Special polynomials associated with rational solutions of the second Painlev'e equation and other equations of its hierarchy are studied. A new method, which allows one to construct each family of polynomials is presented. The structure of…
Special polynomials associated with rational solutions of the second Painlev\'{e} equation and other members of its hierarchy are discussed. New approach, which allows one to construct each polynomial is presented. The structure of the…
Rational solutions of the fourth order analogue to the Painlev'e equations are classified. Special polynomials associated with the rational solutions are introduced. The structure of the polynomials is found. Formulas for their coefficients…
A method for finding relations for the roots of polynomials is presented. Our approach allows us to get a number of relations for the zeros of the classical polynomials and for the roots of special polynomials associated with rational…
Polynomials related to rational solutions of Painleve' equations satisfy certain difference equations. Conditions are given to acertain that all solutions really are polynomials.
We study the Yablonskii-Vorob'ev polynomials, which are special polynomials used to represent rational solutions of the second Painlev\'e equation. Divisibility properties of the coefficients of these polynomials, concerning powers of 4,…
Rational solutions and special polynomials associated with the generalized K_2 hierarchy are studied. This hierarchy is related to the Sawada-Kotera and Kaup-Kupershmidt equations and some other integrable partial differential equations…
Generalized Vorob'ev-Yablonski polynomials have been introduced by Clarkson and Mansfield in their study of rational solutions of the second Painlev\'e hierarchy. We present new Hankel determinant identities for the squares of these special…
We tackle the regularisation of a differential system related to generalised Krawtchouk polynomials. We show a straightforward connection between certain auxiliary quantities involving the recurrence coefficients of these polynomials and…
We consider semiclassical orthogonal polynomials on the unit circle associated with a weight function that satisfy a Pearson-type differential equation involving two polynomials of degree at most three. Structure relations and difference…
New bispectral polynomials orthogonal on a quadratic bi-lattice are obtained from a truncation of Wilson polynomials. Recurrence relation and difference equation are provided. The recurrence coefficients can be encoded in a perturbed…
A relationship between Painleve systems and infinite-dimensional integrable hierarchies is studied. We derive a class of higher order Painleve systems from Drinfeld-Sokolov (DS) hierarchies of type A by similarity reductions. This result…
Hirota's discrete KdV equation is a well-known integrable two-dimensional partial difference equation regarded as a discrete analogue of the KdV equation. In this paper, we show that a variation of Hirota's discrete KdV equation with an…
For a pair of coupled Painlev\'e equations obtained as a similarity reduction of the Hirota-Satsuma systems we describe special parameter-families of solutions given in terms of mixtures of rational and Airy functions, and in terms of a…
In this paper, we consider several special polynomials related to associated sequences of polynomials. Finally, we give some new and interesting identities of those polynomials arising from transfer formula for the associated sequences.
We look for spectral type differential equations for the generalized Jacobi polynomials and for the Sobolev-Laguerre polynomials. We use a method involving computeralgebra packages like Maple and Mathematica and we will give some…
We study the real roots of the Yablonskii-Vorob'ev polynomials, which are special polynomials used to represent rational solutions of the second Painlev\'e equation. It has been conjectured that the number of real roots of the nth…
Orthogonal polynomials and multiple orthogonal polynomials are interesting special functions because there is a beautiful theory for them, with many examples and useful applications in mathematical physics, numerical analysis, statistics…
In this paper, we derive some new and interesting idebtities for Bernoulli, Euler and Hermite polynomials associated with Chebyshev polynomials.