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Computation of Legendre functions

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Abstract

The computation of the Legendre functions Pv(x) for −1 < x ≤ 1, v ∈ ℂ and of the adjoint Legendre functions P −mv (x) for −1 < x ≤ 1, v ∈ ℂ, and m ∈ ℤ+ is the subject of the paper. Bibliography: 5 titles.

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References

  1. I. M. Ryzhik and I. S. Gradshtein, Tables of Integrals, Sums, Series, and Products [in Russian], Moscow (1951).

  2. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis [Russian translation], Moscow (1963).

  3. B. A. Samokish, “A remark on the computation of definite integrals,” in: Methods of Computing, LGU (1963), pp.45–49.

  4. V. A. Fock, “On the representation of an arbitrary function in the form of an integral of the Legendre function with a complex index,” Dokl. Akad. Nauk SSSR, 39, No. 7 (1943), 279–283.

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  5. V. M. Babich and K. D. Cherednichenko, “On Fock type asymptotics of Legendre functions,” Integr. Transf. Spec. Funct., 5(1–2), 1–18 (1997).

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Correspondence to V. M. Babich.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 342, 2007, pp. 14–30.

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Babich, V.M., Dement’ev, D.B. & Samokish, B.A. Computation of Legendre functions. J Math Sci 148, 639–649 (2008). https://doi.org/10.1007/s10958-008-0014-3

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  • DOI: https://doi.org/10.1007/s10958-008-0014-3

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