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MR669656 (83k:33027) 33A70 (33-04)
Kölbig, K. S. Closed expressions for $\int \sp{1}\sb{0}t\sp{-1}{\rm log}\sp{n-1}\ t\log\sp{p}(1-t)\,dt$. Math. Comp. 39 (1982), no. 160, 647–654.
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