Workshop: A non-hypergeometric E-function

Date: 2021-10-19

Time: 09:45 - 10:45

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Javier Frésan


In a landmark 1929 paper, Siegel introduced the class of E-functions with the goal of generalising the transcendence theorems for the values of the exponential. E-functions are power series with algebraic coefficients subject to certain growth conditions that satisfy a linear differential equation. Besides the exponential, examples include Bessel functions and a rich family of hypergeometric series. Siegel asked whether all E-functions are polynomial expressions in these hypergeometric series. I will explain why the answer is negative (joint work with Peter Jossen).