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