an:05636954
Zbl 1178.33022
Zhedanov, Alexei
Elliptic polynomials orthogonal on the unit circle with a dense point spectrum
EN
Ramanujan J. 19, No. 3, 351-384 (2009).
00253308
2009
j
33E05 33C47 42C05 33E30
Summary: We introduce two explicit examples of polynomials orthogonal on the unit circle. Moments and the reflection coefficients are expressed in terms of the Jacobi elliptic functions. We find explicit expression for these polynomials in terms of elliptic hypergeometric functions. We show that the obtained polynomials are orthogonal on the unit circle with respect to a dense point measure. We also construct corresponding explicit systems of polynomials orthogonal on the interval of the real axis with respect to a dense point measure. They can be considered as an elliptic generalization of the Askey-Wilson polynomials of a special type.