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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On the numerical evaluation of Legendre’s chi-function
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by J. Boersma and J. P. Dempsey PDF
Math. Comp. 59 (1992), 157-163 Request permission

Abstract:

Legendre’s chi-function, ${\chi _n}(z) = \Sigma _{k = 0}^\infty {z^{2k + 1}}/{(2k + 1)^n}$, is reexpanded in a power series in powers of $\log z$. The expansion obtained is well suited for the computation of ${\chi _n}(z)$ in the two cases of real z close to 1, and $z = {e^{i\alpha }},\alpha \in \mathbb {R}$. For $n = 2$ and $n = 3$, the present computational procedure is shown to be superior to the procedure recently proposed by Dempsey, Liu, and Dempsey, which uses Plana’s summation formula.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Math. Comp. 59 (1992), 157-163
  • MSC: Primary 65B10
  • DOI: https://doi.org/10.1090/S0025-5718-1992-1134715-0
  • MathSciNet review: 1134715