The “classical” Laurent biorthogonal polynomials
نویسندگان
چکیده
منابع مشابه
Elliptic hypergeometric Laurent biorthogonal polynomials with a dense point spectrum on the unit circle
We construct new elliptic solutions of the qd-algorithm. These solutions can be interpreted as elliptic solutions of the discrete-time Toda chain as well. As a by-product, we obtain new explicit orthogonal and biorthogonal polynomials in terms of the elliptic hypergeometric function 3G2(z). Their recurrence coefficients are expressed in terms of the elliptic functions. 1991 Mathematics Subject ...
متن کاملA Combinatorial Representation with Schroder Paths of Biorthogonality of Laurent Biorthogonal Polynomials
Combinatorial representation in terms of Schröder paths and other weighted plane paths are given of Laurent biorthogonal polynomials (LBPs) and a linear functional with which LBPs have orthogonality and biorthogonality. Particularly, it is clarified that quantities to which LBPs are mapped by the corresponding linear functional can be evaluated by enumerating certain kinds of Schröder paths, wh...
متن کاملDecompositions of Laurent Polynomials
In the 1920’s, Ritt studied the operation of functional composition g ◦ h(x) = g(h(x)) on complex rational functions. In the case of polynomials, he described all the ways in which a polynomial can have multiple ‘prime factorizations’ with respect to this operation. Despite significant effort by Ritt and others, little progress has been made towards solving the analogous problem for rational fu...
متن کاملA Combinatorial Derivation with Schroder Paths of a Determinant Representation of Laurent Biorthogonal Polynomials
A combinatorial proof in terms of Schröder paths and other weighted plane paths is given for a determinant representation of Laurent biorthogonal polynomials (LBPs) and that of coefficients of their three-term recurrence equation. In this process, it is clarified that Toeplitz determinants of the moments of LBPs and their minors can be evaluated by enumerating certain kinds of configurations of...
متن کاملBiorthogonal Laurent polynomials, Töplitz determinants, minimal Toda orbits and isomonodromic tau functions
We consider the class of biorthogonal polynomials that are used to solve the inverse spectral problem associated to elementary co-adjoint orbits of the Borel group of upper triangular matrices; these orbits are the phase space of generalized integrable lattices of Toda type. Such polynomials naturally interpolate between the theory of orthogonal polynomials on the line and orthogonal polynomial...
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: Journal of Computational and Applied Mathematics
سال: 1998
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(98)00118-6