# Addition formula for big q-Legendre polynomials

Research paper by Erik Koelink

Indexed on: 25 Apr '94Published on: 25 Apr '94Published in: Mathematics - Quantum Algebra

#### 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.