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arXiv · 1606.02642

Jacobi series for general parameters and applications

Rodica D. Costin·Marina David
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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.

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Rodica D. Costin, Marina David. 2016-06-08. Jacobi series for general parameters and applications. https://arxiv.org/abs/1606.02642

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