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The evaluation of Legendre functions of the second kind

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Abstract

A method of evaluating Legendre functions of the second kind by applying the trapezoidal rule to Heine's integral representation is described. An error analysis is given, and some numerical results are obtained.

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References

  1. M. Abramowitz and I.A. Stegun,Handbook of Mathematical Functions (Dover, New York, 1965).

    Google Scholar 

  2. C. Chiarella and A. Reichel, On the evaluation of integrals related to the error function, Math. Comp. 22 (1968) 137–143.

    Google Scholar 

  3. E.T. Copson,An Introduction to the Theory of Functions of a Complex Variable (Oxford University Press, 1935).

  4. H.E. Fettis, Numerical calculation of certain definite integrals by Poisson's summation formula, MTAC 9 (1955) 85–92.

    Google Scholar 

  5. D.B. Hunter, The calculation of certain Bessel functions, Math. Comp. 18 (1964) 123–128.

    Google Scholar 

  6. D.B. Hunter, Some Gauss-type formulae for the evaluation of Cauchy principal values of integrals, Numer. Math 19 (1972) 419–424.

    Google Scholar 

  7. D.B. Hunter and G.E. Okecha, A modified Gaussian quadrature rule for integrals involving poles of any order, BIT 26 (1986) 233–240.

    Google Scholar 

  8. D.B. Hunter and T. Regan, A note on the evaluation of the complementary error function, Math. Comp. 26 (1972) 539–541.

    Google Scholar 

  9. E. Jahnke and F. Emde (revised by F. Lösch),Tables of Higher Functions (McGraw-Hill, New York, 1960).

    Google Scholar 

  10. Y.L. Luke, Simple formulas for the evaluation of some higher transcendental functions, J. Math. Phys. 34 (1956) 298–307.

    Google Scholar 

  11. Y.L. Luke,The Special Functions and their Approximation, Vol. 2 (Academic Press, New York, 1969).

    Google Scholar 

  12. F. Matta and A. Reichel, Uniform computation of the error function and other related functions, Math. Comp. 25 (1971) 339–344.

    Google Scholar 

  13. J. McNamee, Error bounds for the evaluation of integrals by the Euler-Maclaurin formula and by Gauss-type formulae, Math. Comp 18 (1964) 368–381.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Bradford, Bradford, West Yorkshire, England

    D. B. Hunter

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  1. D. B. Hunter
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Dedicated to Professor Luigi Gatteschi

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Hunter, D.B. The evaluation of Legendre functions of the second kind. Numer Algor 10, 41–49 (1995). https://doi.org/10.1007/BF02198295

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  • DOI: https://doi.org/10.1007/BF02198295

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