Integrals that can be represented as linear forms of generalized polylogarithms. (English. Russian original) Zbl 1049.11077

Zlobin, S. A.

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.

Reviewer: Masanori Morishita (Kanazawa)

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