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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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Construction of holomorphic function

I was trying to construct a holomorphic function $f$ on $\mathbb{C}$ such that $|f|^2(z)=e^{(|z|^2-\frac{1}{2})^2}$. I will be happy if someone can give me an idea how to do that. I would like also t …
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