Closed expressions for ∫¹₀𝑡⁻¹𝑙𝑜𝑔ⁿ⁻¹𝑡log^{𝑝}(1-𝑡)𝑑𝑡

Kölbig, K. S.

doi:10.1090/S0025-5718-1982-0669656-X

Closed expressions for $\int \sp{1}\sb{0}t\sp{-1}{\rm log}\sp{n-1}\ t\log\sp{p}(1-t)\,dt$

Author: K. S. Kölbig
Journal: Math. Comp. 39 (1982), 647-654
MSC: Primary 33A70; Secondary 33-04
DOI: https://doi.org/10.1090/S0025-5718-1982-0669656-X
MathSciNet review: 669656
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Abstract: Closed expressions for the integral $\smallint _0^1{t^{ - 1}}{\log ^{n - 1}}t{\log ^p}(1 - t)\;dt$ , whose general form is given elsewhere, are listed for , . A formula is derived which allows an easy evaluation of these expressions by formula manipulation on a computer.

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