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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.

4 votes

A closed formula for a sum involving hypergeometric function

The formula is wrong (except some special cases like for $x=0$). The left hand side (LHS) is symmetric in $x$ and $y$. This would imply a symmetry of the RHS. $${ }_1F_1(\beta,\alpha+1, x) U(\beta,\al …
Christian Sattlecker's user avatar