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- Title
Rings of formal power series and a multidimensional analogue of the lagrange formula.
- Authors
Graev, M. I.
- Abstract
The article presents the multidimensional analogue of the Langrage formula in the rings formal power series. It provides the derivation of Lagrange formula based on properties of holomorphic functions and is determined by the convergent series where f(y) is any function holomorphic in a neighborhood of the point y = 0 and y(x) holomorphic in a neighborhood of the point x = 0 to the equation y = xf(y). It notes the description of solutions of system in formal series presented as infinite sums of monomials and the residue of formal series as well as in the space of Laurent P-series and the transformation of P-series. Moreover, the solution of the general system of equations is offered in which the theorem on residue preservation is applied.
- Subjects
NUMERICAL solutions to Lagrange equations; POWER series rings; LAGRANGE spaces; NUMERICAL calculations; MATHEMATICAL analysis; STOCHASTIC convergence; HOLOMORPHIC functions; MATHEMATICAL transformations; EXISTENCE theorems
- Publication
Doklady Mathematics, 2011, Vol 84, Issue 1, p459
- ISSN
1064-5624
- Publication type
Article
- DOI
10.1134/S1064562411040089