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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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Distribution of zeros

Suppose $f(z) = P(z)e^{Q(z)}$ where $P,Q$ are real polynomials. What is the number of non-real zeros of $f^{(k)}$ as $k$ increases? We know that $f''$ has $\geq m$ zeros where $m$ depends on $Q(z)$. …