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for-x-0-let-x-x-x-1-prove-that-x-1-x-x-n-1-1-n-x-n-2-ptove-that-1-3-prove-that-0-e-x-ln-x-dx-

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Question Number 33345 by prof Abdo imad last updated on 14/Apr/18
for x∈]0,+∞[ let ψ(x) = ((Γ^′ (x))/(Γ(x))) 1)prove that ψ(x) =−(1/x) −γ +x Σ_(n=1) ^∞ (1/(n(x+n))) 2)ptove that γ =−Γ^′ (1) 3) prove that ∫_0 ^∞ e^(−x) ln(x)dx =−γ .
forx∈]0,+∞[letψ(x)=Γ′(x)Γ(x)1)provethatψ(x)=−1x−γ+x∑n=1∞1n(x+n)2)ptovethatγ=−Γ′(1)3)provethat∫0∞e−xln(x)dx=−γ.

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