let s>1 be a real number. for all continues function f:[0,1]→R
such that ∫_( 0) ^( 1) f(x)=0, determind of the exist a
positive constant K(s) statisfying:
(∫_0 ^( 1) f(x)∙Li_s (x)dx)^2 ≥K(s)∫_( 0) ^( 1) (f(x))^2 ∙Li_(2s−1 )
where Li_s (x)=Σ_(k=1) ^∞ (x^k /k^s ) is the polylogarithm function.
if such a constants exists, find the optimal value of K(s).
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