A class of hypergeometric polynomials with zeros on the unit circle: Extremal and orthogonal properties and quadrature formulas

作者：Dimitrov D K; Ismail M E H; Ranga A Sri^*

来源：Applied Numerical Mathematics, 2013, 65: 41-52.

DOI：10.1016/j.apnum.2012.11.002

• Hypergeometric polynomials
• Para-orthogonal polynomials
• Quadrature rules

The class of hypergeometric polynomials F-2(1) (-m, b; b + (b) over bar; 1 - z) with respect to the parameter b = lambda + i eta, where lambda %26gt; 0, are known to have all their zeros simple and exactly on the unit circle vertical bar z vertical bar = 1. In this note we look at some of the associated extremal and orthogonal properties on the unit circle and on the interval (-1, 1). We also give the associated Gaussian type quadrature formulas.

• 出版日期2013-3