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On the Evaluation of Correction Terms of Gaussian Integration
January/February 2011 (vol. 13 no. 1)
pp. 58-61
Mohankumar Nandagopal, Indira Gandhi Centre for Atomic Research

An accurate and compact computing recipe for evaluating correction terms for the Gaussian integration of analytic functions offers economy and high accuracy for many integrals of interest in physical sciences.

1. W.W. Bell, Special Functions for Scientists and Engineers, D. Van Nostrand, 1968.
2. A. Natarajan and N. Mohankumar, "An Accurate Method for the Generalized Fermi-Dirac Integral," Computer Physics Communications, vol. 137, no. 3, 2001, pp. 361–365.
3. P.J. Davis and P. Rabinowitz, Methods of Numerical Integration, 2nd ed., Academic Press, 1984.
4. P.J. Davis, "Errors of Numerical Approximation for Analytic Functions," J. Rational Mechanical Analysis, vol. 2, 1953, pp. 303–313.
5. W. Barrett, "Convergence Properties of Gaussian Quadrature Formulae," Computer J., vol. 3, 1961, pp. 272–277.
6. F.G. Lether, "Subtracting out Complex Singularities in Numerical Integration," Math. Computation, vol. 31, no. 4, 1977, pp. 223–229.
7. M.M. Chawla and M.K. Jain, "Error Estimates for Gauss Quadrature Formulas for Analytic Functions," Math. Computation, vol. 22, 1968, pp. 82–90.
8. A. Erdelyi et al., Higher Transcendental Functions, vol. 2, McGraw-Hill, 1953.
9. L.C. Baker, C Mathematical Function Library, McGraw-Hill, 1991.
10. N. Mohankumar, S. Sen, and R. Ramar, "On the Evaluation of Correction Terms in Gauss-Legendre Quadrature," Computer Physics Comm., vol. 181, no. 1, 2010, pp. 17–20.
11. S. Barnard and J.M. Child, Higher Algebra, Macmillan, 1952.

Index Terms:
Gaussian integration, meromorphic functions, singularity, correction
Mohankumar Nandagopal, "On the Evaluation of Correction Terms of Gaussian Integration," Computing in Science and Engineering, vol. 13, no. 1, pp. 58-61, Jan.-Feb. 2011, doi:10.1109/MCSE.2011.12
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