Associated Jacobi-Laurent polynomials

摘要

The Jacobi-Laurent polynomials have been introduced by Hendriksen and van Rossum (1986). In the present paper explicit formulas for the orthogonal Laurent polynomials satisfying the recurrency for the Jacob-Laurent polynomials with n replaced by n + b are given. These new orthogonal Laurent polynomials are called “associated Jacobi-Laurent polynomials”. Using these associated Laurent polynomials, the denominator and the numerator of certain two-point Padé approximants to the pair of functions z F(a,b +1; c+b+1;z)F(a,b; c+b; z) at O and c+b-a+b+1F(−c+1, b+1; −a+b+2;z−1)F(−c+1,b+1;z−l)at ∞ are given. Also some confluent cases are considered.