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Multiple hypergeometric series and polyzetas. (Séries hypergéométriques multiples et polyzêtas.) (French) Zbl 1161.33003
The authors of this important paper offer a theoretical and effective algorithm for decomposition as linear combinations of multiple zeta values of certain general hypergeometric series and integrals. Such results have a major importance e.g. in the difficult theory of linear independence study of the classical zeta function value. The results are too involved to be stated here.

MSC:
11M32 Multiple Dirichlet series and zeta functions and multizeta values
33C70 Other hypergeometric functions and integrals in several variables
11J72 Irrationality; linear independence over a field
33B30 Higher logarithm functions
33C20 Generalized hypergeometric series, \({}_pF_q\)
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