Orthogonality of Jacobi and Laguerre polynomials for general parameters via the Hadamard finite part
Abstract
Orthogonality of the Jacobi and of Laguerre polynomials, Pn(a,b) and Ln(a), is established for a,b complex (a,b not negative integers and a+b different from -2,-3,...) using the Hadamard finite part of the integral which gives their orthogonality in the classical cases. Riemann-Hilbert problems that these polynomials satisfy are found. The results are formally similar to the ones in the classical case (when the real parts of a,b are greater than -1)
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