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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.

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Entire solutions of polynomial ODE's

One way to see that the local holomorphic function $f$ is entire is to see if the ODE defined by the polynomial $P$ is integrable. If its not, then you can assure that the solutions are not entire due …
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