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Integrals that can be represented as linear forms of generalized polylogarithms. (English. Russian original) Zbl 1049.11077
Math. Notes 71, No. 5, 711-716 (2002); translation from Mat. Zametki 71, No. 5, 782-787 (2002).
The author introduces two kinds of integrals $$V(z)$$ and $$S(z)$$, where $$V(z)$$ generalizes Beukers-Vasilenko’s integrals, which have a close connection with multiple zeta values, and $$S(z)$$ is a generalization of Sorokin’s integrals. Then he establishes the connection between $$V(z)$$ and $$S(z)$$, and further expresses $$S(z)$$ as a linear form of generalized polylogarithms.

##### MSC:
 11J72 Irrationality; linear independence over a field 11G55 Polylogarithms and relations with $$K$$-theory 11M06 $$\zeta (s)$$ and $$L(s, \chi)$$ 33B30 Higher logarithm functions
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