Please use this identifier to cite or link to this item:
Title: Sèries de Taylor de zeros de polinomis d’exponents complexos
Author: Quingles i Davı́, Guillem
Director/Tutor: D'Andrea, Carlos, 1973-
Keywords: Combinatòria (Matemàtica)
Treballs de fi de grau
Funcions de diverses variables complexes
Funcions holomorfes
Bachelor's theses
Functions of several complex variables
Holomorphic functions
Issue Date: 20-Jun-2021
Abstract: [en] We follow the work of DeFranco in [4] and [5] to prove a factorization formula for the Taylor series coefficients of a zero of a polynomial as a function of the polynomial’s coefficients. This result extends to more general functions which we call complex exponent polynomials and also to the sum of a complex exponent polynomial and an holomorphic function with a simple zero. To prove this formula we need lemmas about Stirling numbers, multisets and partition sets. We also show that, when applied to polynomials, the formula recovers Sturmfels results in [11]. Finally, continuing the the work of DeFranco, we see that the formula, when applied to second degree polynomials, agrees with the known radical solutions and we prove an extension of a result about derivations on commutative rings.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Carlos D'Andrea
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

Files in This Item:
File Description SizeFormat 
tfg_quingles_davi_guillem.pdfMemòria742.41 kBAdobe PDFView/Open

This item is licensed under a Creative Commons License Creative Commons