Uniform Asymptotic Expansion for a Class of Polynomials Biorthogonal on the Unit Circle

摘要

A family of orthogonal polynomials on the disk unit with respect to the classical weight function is considered. The fact that the zeros of the weight functions can explain the asymptotic behavior of orthogonal or biorthogonal polynomials is studied. A uniform asymptotic expansion for this family of polynomials biorthogonal on the unit circle is given. The result is valid for the parameter over compact subsets of complex numbers without zero. This result is not valid for all hypergeometric functions.