Coefficient Extraction Formula and Furstenberg's Theorems
Yining Hu
TL;DR
This paper generalizes the coefficient extraction formula for algebraic series across all fields, extending Furstenberg's theorem and including the Flajolet-Soria formula as a special case.
Contribution
It introduces a universal coefficient extraction formula for algebraic series based on Furstenberg's proposition, applicable to all fields.
Findings
Unified coefficient extraction formula for algebraic series
Extension of Flajolet-Soria formula to all fields
Validation of the formula using Furstenberg's theorem
Abstract
In this article, using a Proposition of Furstenberg, we give a coefficient extraction formula for algebraic series that is valid for all fields, of which the Flajolet-Soria coefficient extraction formula for the complex field is a special case.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Differential Equations and Dynamical Systems · Nonlinear Waves and Solitons