INTEGRAL REPRESENTATIONS FOR THE JACOBI–PINEIRO POLYNOMIALS AND THE FUNCTIONS OF THE SECOND KIND

Abstract

We consider the Hermite – Pad´e approximants for the Cauchy transforms of the Jacobi weights in one interval. The denominators of the approximants are known as Jacobi – Pi˜neiro polynomials. These polynomials, together with the functions of the second kind, satisfy a generalized hypergeometric differential equation. In the case of the two weights, we construct the basis of the solutions of this ODE with elements of different growth rate. We obtain the integral representations for the basis elements.

Keywords

• hermite – pad´e approximants
• jacobi – pi˜neiro multiple orthogonal polynomials
• functions of the second kind
• integral representations
• generalized hypergeometric functions