Demonstrates algebraic independence in Airy functions, suggesting implications for transcendental number theory.
Using tools from the Siegel-Shidlovskii theory of transcendental numbers, we prove that a nontrivial solution of the Airy equation, its derivative, and an antiderivative are algebraically independent over the field of rational functions. Courtesy of Michael Singer, the result is also derived from general considerations in differential Galois theory.
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Folkmar Bornemann (2026) studied this question.
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