Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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



On the numerical evaluation of Legendre's chi-function

Authors: J. Boersma and J. P. Dempsey
Journal: Math. Comp. 59 (1992), 157-163
MSC: Primary 65B10
MathSciNet review: 1134715
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] M. Abramowitz and I. A. Stegun, Handbook of mathematical functions, Dover, New York, 1965.
  • [2] K. M. Dempsey, D. Liu, and J. P. Dempsey, Plana's summation formula for $ \Sigma _{m = 1,3, \ldots }^\infty {m^{ - 2}}\sin (m\alpha ),{m^{ - 3}}\cos (m\alpha ),{m^{ - 2}}{A^m},{m^{ - 3}}{A^m}$, Math. Comp. 55 (1990), 693-703. MR 1035929 (91b:65003)
  • [3] A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher transcendental functions, Vol. I, McGraw-Hill, New York, 1953.
  • [4] W. Gautschi, On certain slowly convergent series occurring in plate contact problems, Math. Comp. 57 (1991), 325-338. MR 1079018 (91j:40002)
  • [5] L. Lewin, Polylogarithms and associated functions, North-Holland, New York, 1981. MR 618278 (83b:33019)
  • [6] H. Li, Unbonded contact of rectangular plates on edge supports or elastic foundations, Ph.D. Thesis, Clarkson University, Potsdam, 1988.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65B10

Retrieve articles in all journals with MSC: 65B10

Additional Information

Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society