Orthogonality of Jacobi and Laguerre polynomials for general parameters via the Hadamard finite part

Details Orthogonality of Jacobi and Laguerre polynomials for general parameters via the Hadamard finite part Orthogonality of Jacobi and Laguerre polynomials for general parameters via the Hadamard finite part

2009-01-19

arxiv.org/abs/0901.2940v1

Mathematics

Classical Analysis and ODEs

14 pages

Scientific paper

Orthogonality of the Jacobi and of Laguerre polynomials, P_n^(a,b) and L_n^(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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