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We give explicit expressions (or at least an algorithm of obtaining suchexpressions) of the coefficients of the Laurent series expansions of theEuler-Zagier multiple zeta-functions at any integer points. The main tools arethe Mellin-Barnes integral formula and the harmonic product formulas. TheMellin-Barnes integral formula is used in the induction process on the numberof variables, and the harmonic product formula is used to show that the Laurentseries expansion outside the domain of convergence can be obtained from thatinside the domain of convergence.

Laurent series expansions of multiple zeta-functions of Euler-Zagier type at integer points