Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9505818 | Advances in Applied Mathematics | 2005 | 23 Pages |
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.
Keywords
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Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Guoce Xin,