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Many special functions appear as solutions of differential equations or integrals of elementary functions. Most special functions have relationships with representation theory of Lie groups.

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Does there exist an upper bound on the Fourier coefficients of the reciprocal theta function...

As @TerryTao stated correctly in the comments, a bound on the Fourier coefficients can be obtained by the saddle point method: The extension of $\frac 1 \theta$ to a meromorphic function on $\mathbb C …
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