Algebraic properties of (sic)-functions

In [3] Andre showed that the minimal differential equations of (sic)-functions and E -functions have a basis of holomorphic solutions at every point except for zero and infinity. In addition, in [5] he observed that if f(1)(z) is an E-function with rational coefficients such that f(1)(1) = 0, then f(1)(z)/(z - 1) is also an E-function. With this additional result Andre derived transcendence results for the values of E-functions. These results were further applied by Beukers [7] to obtain a strengthened Siegel-Shidlovskii theorem for E -functions. The arguments of Andre and Beukers should aid in obtaining a Siegel-Shidlovskii type theorem for 9-functions provided that one can show that if f-1(z) is a (sic)-function with rational coefficients such that the 1-summation F-1(z) vanishes at z = 1, then f-1(z)/(z - 1) is also a (sic)-function. In this paper, we investigate this problem and derive several criteria to check its validity. (C) 2021 Elsevier Inc. All rights reserved.