Abstract
In this paper, we establish a residue theorem for Malcev–Neumann series that requires few constraints, and includes previously known combinatorial residue theorems as special cases. Our residue theorem identifies the residues of two formal series (over a field of characteristic zero) which are related by a change of variables. We obtain simple conditions for when a change of variables is possible, and find that the two related formal series in fact belong to two different fields of Malcev–Neumann series. The multivariate Lagrange inversion formula is easily derived and Dyson's conjecture is given a new proof and generalized.
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