FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 6, PAGES 33-39

**On the weakened Siegel's conjecture**

V. A. Gorelov

Abstract

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In the paper, we prove that two definitions of $E$-functions present in
mathematics are equivalent if $E$-functions satisfy
second-order linear differential equations.
For this set of functions, a weakened variant of the well-known
Siegel conjecture about representability of any $E$-function by
a polynomial of hypergeometric functions is also proved.

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Last modified: January 13, 2006