✦ LIBER ✦

A Combinatorial Formula for the Linearization Coefficients of General Sheffer Polynomials

✍ Scribed by Dongsu Kim; Jiang Zeng

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 341 KB
Volume: 22
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.2000.0459

No coin nor oath required. For personal study only.

✦ Synopsis

We prove a formula for the linearization coefficients of the general Sheffer polynomials, which unifies all the special known results for Hermite, Charlier, Laguerre, Meixner and Meixner-Pollaczek polynomials. Furthermore, we give a new and explicit real version of the corresponding formula for Meixner-Pollaczek polynomials. Our proof is based on some explicit bijections and sign-reversing weight-preserving involutions.

📜 SIMILAR VOLUMES

The Combinatorics of Meixner Polynomials

The Combinatorics of Meixner Polynomials: Linearization Coefficients

✍ A. de Médicis 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 202 KB

We describe various aspects of the Meixner polynomials. These include combinatorial descriptions of the moments, the orthogonality relation, and the linearization coefficients.

A Formula for the General Solution of a

A Formula for the General Solution of a Constant-coefficient Difference Equation

✍ D.A. Wolfram 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 176 KB

We give a formula for the general solution of a dth-order linear difference equation with constant coefficients in terms of one of the solutions of its associated homogeneous equation. The formula neither uses the roots of the characteristic equation nor their multiplicities. It can be readily gener

Proof of the recurrence formula for the

Proof of the recurrence formula for the distributed equidistant linear phase polynomial

✍ S. Tlrtoprodjo 📂 Article 📅 1974 🏛 John Wiley and Sons 🌐 English ⚖ 153 KB

A Basis for Polynomial Solutions to Syst

A Basis for Polynomial Solutions to Systems of Linear Constant Coefficient PDE's

✍ Paul S. Pedersen 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 261 KB

Let K represent either the real or the complex numbers. Let P k , k=1, 2, ..., r be constant coefficient (with coefficients from K) polynomials in n variables and let r] be the set of all polynomial solutions (of degree M) to this system of partial differential equations. We solve the problem of fi

On the Generation of Orthogonal Polynomi

On the Generation of Orthogonal Polynomials Using Asymptotic Methods for Recurrence Coefficients

✍ Andrew S. Clarke; Bernie Shizgal 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 468 KB

A Combinatorial Proof of a Recursion for

A Combinatorial Proof of a Recursion for the q-Kostka Polynomials

✍ Kendra Killpatrick 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 196 KB

The Kostka numbers K \* + play an important role in symmetric function theory, representation theory, combinatorics and invariant theory. The q-Kostka polynomials K \* + (q) are the q-analogues of the Kostka numbers and generalize and extend the mathematical meaning of the Kostka numbers. Lascoux an