PolyGammaSimplify[expr] transforms polygamma functions in expr, trying to either decrease the number of polygamma functions, or convert combinations of them into more elementary functions.
PolyGammaSimplify is automatically used inside FullSimplify and FunctionExpand.
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PolyGammaSimplify[expr] transforms polygamma functions in expr, trying to either decrease the number of polygamma functions, or convert combinations of them into more elementary functions. 
