Some Explicit Biorthogonal Polynomials

نویسندگان

  • D. S. Lubinsky
  • H. Stahl
چکیده

Let α > 0 and ψ (x) = x. Let Sn,α be a polynomial of degree n determined by the biorthogonality conditions Z 1 0 Sn,αψ j = 0, j = 0, 1, . . . , n− 1. We explicitly determine Sn,α and discuss some other properties, including their zero distribution. We also discuss their relation to the Sidi polynomials. §

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

ar X iv : m at h / 98 04 02 7 v 1 [ m at h . C A ] 6 A pr 1 99 8 BIORTHOGONAL ENSEMBLES

Abstract. One object of interest in random matrix theory is a family of point ensembles (random point configurations) related to various systems of classical orthogonal polynomials. The paper deals with a one–parametric deformation of these ensembles, which is defined in terms of the biorthogonal polynomials of Jacobi, Laguerre and Hermite type. Our main result is a series of explicit expressio...

متن کامل

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 کامل

On Bilateral Generating Functions of Konhauser Biorthogonal Polynomials

In this article, we have obtained some novel results on bilateral generating functions of the polynomials, YYnn+rr αα−nnnn(xx;kk), a modified form of Konhauser biorthogonal polynomials, YYnn(xx; kk) by group-theoretic method. As special cases, we obtain the corresponding results on Laguerre polynomials, LLnn αα(xx). Some applications of our results are also discussed.

متن کامل

SUSLOV: The q-harmonic oscillator and the Al-Salam and Carlitz polynomials

One more model of a q-harmonic oscillator based on the q-orthogonal polynomials of Al-Salam and Carlitz is discussed. The explicit form of q-creation and q-annihilation operators, q-coherent states and an analog of the Fourier transformation are established. A connection of the kernel of this transform with a family of self-dual biorthogonal rational functions is observed.

متن کامل

. C A ] 9 J ul 1 99 3 The q - Harmonic Oscillator and an Analog of the Charlier polynomials

A model of a q-harmonic oscillator based on q-Charlier poly-nomials of Al-Salam and Carlitz is discussed. Simple explicit realization of q-creation and q-annihilation operators, q-coherent states and an ana-log of the Fourier transformation are found. A connection of the kernel of this transform with biorthogonal rational functions is observed. Models of q-harmonic oscillators are being develop...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005