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Evaluation of Integrals
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algebra analytic approximation arbitrary asymptotic base vectors Bessel functions Bessel's equation boundary conditions called Chapter coefficients components consider constant contour converges coordinate system covariant derivative curve defined diagonal differential equation differential operator dimensionality discussed dispersion relation distribution drum head eigenfunctions eigenvalue eigenvalue problem eigenvectors elliptic error Euler-Lagrange equation evaluate example Find finite formula Fourier series Fourier transform function f(x Gaussian given gives Green's function group element Hermitian homogeneous hypergeometric independent infinite inhomogeneous integral equation integral representation integrand inverse irreducible representations kernel Laplace transform Legendre Legendre polynomials matrix method multiply normal obeys obtain orthogonal parameters path physical plane pole polynomial probability real axis recursion relation region result rotation scalar Section separation of variables shown in Figure solution solve spherical Suppose symmetry group temperature tensor theorem theory unitary values vanish variational z-plane zero