Applications of a theorem by A. B. Shidlovski

  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},
  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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