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On the Numerical Evaluation of Legendre's Chi-Function
J. Boersma and J. P. Dempsey
Mathematics of Computation
Vol. 59, No. 199 (Jul., 1992), pp. 157-163
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2152987
Page Count: 7
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Legendre's chi-function, χn(z) = ∑∞k = 0 z2k + 1/(2k + 1)n, is reexpanded in a power series in powers of log z. The expansion obtained is well suited for the computation of χn(z) in the two cases of real z close to 1, and z = eiα, α ∈ R. For n = 2 and n = 3, the present computational procedure recently proposed by Dempsey, Liu, and Dempsey, which uses Plana's summation formula.
Mathematics of Computation © 1992 American Mathematical Society