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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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Is there a specific named function that is the inverse of $x+x^a$ for $x$ real?

This seems such a simple question that I fear I must have missed some elementary maths. I am looking for a way to solve $x+x^a = y$ by reference to an already defined function, $a,x,y > 0$ are real. F …
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