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

Kölbig, K. S.

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

Closed expressions for $\int ^{1}_{0}t^{-1}\textrm {log}^{n-1}\ t\log ^{p}(1-t) dt$

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 $n = 1(1)9$, $p = 1(1)9$. A formula is derived which allows an easy evaluation of these expressions by formula manipulation on a computer.

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