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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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How to know if two special functions are related by an elementary function?

Suppose I have two special functions $f_1$ and $f_2$. Is there an algorithm which can tell me whether there exists elementary $g$ such that $f_1 = g\circ f_2$? Furthermore, is there any possibility to …