Gevrey Classes of the Power Series
Explore Gevrey classes, a powerful framework for understanding the growth of power series coefficients, with insights from Edmond Maillet's theorem on formal solutions to analytical differential equations.
The main result
Dear Reader, in today's brief, I would like to remind about the Gevrey classes of the power series. It is an attempt to classify the growth of coefficients when the series clearly goes wild. The mathematical definition of Gevrey classes is followed by the classical theorem by Edmond Maillet, which states that formal solutions to analytical differential equations cannot go wilder beyond Gevrey classes.
Acknowledgement
Thanks to my friend and collaborator, Dr Ahmad DEEB, who invited me to this fascinating topic. His PhD thesis manuscript is a golden mine on the use of divergent series in numerical analysis:
Dr. Denys Dutykh
Associate Professor of Mathematics
Khalifa University of Science and Technology, Abu Dhabi, UAE
Related Posts
The Hadamard Gap Theorem and Stein Manifolds
How do big gaps in power series relate to Stein manifolds? A look at the Hadamard Gap Theorem and why the unit disk is a Stein manifold.
Applied mathematics has met the machine before
The long version of my guest essay for Proofs and Prompts, published there on 28 September 2026.
Interim Guidance on the Use of AI Tools in Postgraduate Studies and Research
Interim guidance sent to the postgraduate students of our College on using AI tools in coursework, research and the thesis, written in the week of the Navier–Stokes announcement.