Jacobi series for general parameters and applications

Abstract

Representation of analytic functions as convergent series in Jacobi polynomials $P_n^{(a,b)}$ is reformulated using a unified approach for almost all complex $a,b$. The coefficients of the series are given as usual integrals in the classical case (when $\Re a,\Re b>-1$), or by the Hadamard principal part of these integrals when they diverge. As an application it is shown that inhomogeneous hypergeometric equations do generically have a unique solution which is analytic at both singular points in the complex plane.

References in corpus (1)

• Analytic linearization of nonlinear perturbations of Fuchsian systems