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NONHOMOGENEOUS CONFLUENT HYPERGEOMETRIC FUNCTIONS
Nonhomogeneous Whittaker and Parabolic Functions
Nonhomogeneous Hypergeometric Functions
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alternative form arbitrary constants associated homogeneous equation asymptotic expansion becomes Bessel functions boundary conditions C2 are arbitrary Chapter confluent hypergeometric functions consider constants of separation contiguous functions converges corresponding cosh d2V d2V d2V derivatives descending powers dz dz equation d2y Erdelyi expressed in terms Green's function Hv(z hypergeometric equation incomplete beta function Laplace's equation linear differential equation linear equation Lommel functions Lorenz's equation Mathieu functions modified Struve function negative integer nonhomogeneous equation nonhomogeneous hypergeometric function nonhomogeneous Legendre function nonhomogeneous linear differential obtain parabolic cylinder functions partial differential equation particular integral particular solution point at infinity Poisson's equation polynomial positive integer power series recurrence formulas regular singularities right side satisfies the equation separation of variables Similarly sinh solution of Poisson's solving Struve function summarize various properties term by term values variation of parameters wave equation zero