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Note on the Computation of the Bessel Function $ I_n(x)$


Author: Derrick Henry Lehmer
Journal: Math. Comp. 1 (1944), 133-135
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  • [1] Such Bessel functions have been used recently at the statistical laboratory of the University of California in preparation of certain statistical tables to appear in Annals of Math. Statistics. See also: J. Wishart, ``A note on the distribution of the correlation ratio,'' Biometrika, v. 24, 1932, p. 454, formula (27).
  • [2] The most extensive tables of $ {I_n}(x)$ are in B.A.A.S., Math. Tables, v. 6, Bessel Functions, part I, Cambridge, 1937, Tables VI and VIII.
  • [3] J. W. Nicholson, Phil. Mag. s. 6, v. 20, 1910, p. 938-943.
  • [4] The $ Q$'s may be checked by the relation $ {Q_m}(1) = {4^m}$; also $ m(m + 1)\int_0^1 {{t^{3m - 1}}{Q_m}({t^{ - 2}})dt} = {2^{2m + 1}}\vert{B_{m + 1}}\vert$, where $ {B_k}$ is the $ k$th Bernoulli number, in the notation of Lucas.
  • [5] D. F. E. Meissel, Astr. Nach. v. 130, 1892, cols. 363-4.
  • [6] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge 1922, p. 228.


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DOI: https://doi.org/10.1090/S0025-5718-44-99053-8
Article copyright: © Copyright 1944 American Mathematical Society