On Taylor series of zeros with general base function
Complex Variables
2021-03-16 v1
Abstract
We prove a formula for the Taylor series coefficients of a zero of the sum of a complex-exponent polynomial and a base function which is a general holomorphic function with a simple zero. Such a Taylor series is more general than a Puiseux series. We prove an integrality result about these coefficients which implies and generalizes the integrality result of Sturmfels ("Solving algebraic equations in terms of -hypergeometric series". Discrete Math. 210 (2000) pp. 171-181). We also prove a transformation rule for a special case of these Taylor series.
Cite
@article{arxiv.2103.07831,
title = {On Taylor series of zeros with general base function},
author = {Mario DeFranco},
journal= {arXiv preprint arXiv:2103.07831},
year = {2021}
}