On Taylor series of zeros with general base function

Mario DeFranco

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arXiv · 2103.07831

On Taylor series of zeros with general base function

Mario DeFranco

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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 $\mathcal{A}$-hypergeometric series". Discrete Math. 210 (2000) pp. 171-181). We also prove a transformation rule for a special case of these Taylor series.

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BibTeX RIS

Mario DeFranco. 2021-03-14. On Taylor series of zeros with general base function. https://arxiv.org/abs/2103.07831

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