# Applications of a theorem by A. B. Shidlovski

@article{Mahler1968ApplicationsOA,
title={Applications of a theorem by A. B. Shidlovski},
author={K. Mahler},
journal={Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences},
year={1968},
volume={305},
pages={149 - 173}
}
• K. Mahler
• Published 1968
• Mathematics
• Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
Shidlovski’s deep theorem on Siegel E-functions satisfying systems of linear differential equations is applied in this paper to the study of the arithmetic properties of the partial derivatives Ck(z) = 1/k!{∂/∂v}k Jv(z)∣v=0 (k = 0,1,2,3) of the Bessel function J0(z). As a by-product, expressions involving Euler’s constant γ and the constant ζ(3) are obtained for which the transcendency can be established.
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