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Series Solution of Secondorder Linear
Contour Integral Solutions of an Ordinary
Oscillation Theorems and SturmLiouville
10 other sections not shown
assume asymptotic expansion asymptotic power series asymptotic series Bessel equation Bessel functions boundary conditions branch point Chapter choose closed contour coefficients complex plane confluent hypergeometric functions consider constant contour integral coordinates corresponding cosec cosh defined derive eigenfunctions eigenvalue entire function equa equation zw Euler exponentially exponents expression finite follows formula gives half plane Hence or otherwise Hermite polynomials hypergeometric equation Illustration independent solutions integer integrand interval Laguerre polynomial Legendre equation Legendre polynomials limit linear differential equation multiple negative integer negative real axis neighbourhood Non-regular obtain odd integer ordinary point origin orthogonal pair point at infinity polynomial of degree positive integer previous section recurrence relation regular singular point replaced result right-hand side roots second solution sector Similarly sin2 single-valued sinh Sturm-Liouville substitution suppose tion uniformly vanishes Whittaker Whittaker function yields