Addition formula for big q-Legendre polynomials
Erik Koelink
Abstract
From Koornwinder's interpretation of big q-Legendre polynomials as spherical elements on the quantum SU(2) group an addition formula is derived for the big q-Legendre polynomial. The formula involves Al-Salam--Carlitz polynomials, little q-Jacobi polynomials and dual q-Krawtchouk polynomials. For the little q-ultraspherical polynomials a product formula in terms of a big q-Legendre polynomial follows by q-integration. The addition and product formula for the Legendre polynomials are obtained when q tends to 1.
Create a lesson
Related papers
Galois-modular obstructions to the categorification of near-group fusion rings
Víctor Blasco
The Askey-Wilson Function is the Laplace Transform of a Positive Measure
Aaron Agulnick
Associated Varieties of Finite-Group Orbifolds
Andrew Riesen
Haagerup symmetries of the E8 theory and conformal nets at central charge eight
Cédric Arhancet
Centralizers of maps as automorphism groups of Yang--Baxter solutions
Gigel Militaru
Quaternionic and Octonionic Frameworks for Quantum Computation: Mathematical Structures, Models, and Fundamental Limitations
Johan Heriberto Rúa Muñoz, Jorge Eduardo Mahecha Gómez, Santiago Pineda Montoya