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Acad addition theorem Akad algebraic Amer analytic asymptotic expansion behavior Bessel functions biorthogonal chapter coefficients complex constant contour convergence corresponding cosh defined denotes derived elliptic integrals Erdelyi expressed in terms finite Gegenbauer polynomials given harmonic polynomial hence Hermite polynomials hypergeometric functions hypergeometric series incomplete gamma functions integral representations interval Jacobi polynomials Jacobian elliptic functions Jv(z Koschmieder Laguerre polynomials Legendre Legendre's linear linearly independent London Math Meijer Neumann nomials notation obtain orthogonal polynomials orthogonal system parabolic cylinder parameter partial differential equation poles poly polynomial of degree positive power series Proc proved rational function rectangle recurrence relation right-hand side satisfy scalar product second kind sin2 solutions surface harmonics system of orthogonal Szego theory theta functions third kind Trans transformation Tricomi valid values variable vector Watson Weierstrass weight function