Journal of Mathematical Sciences

, Volume 148, Issue 5, pp 639–649 | Cite as

Computation of Legendre functions

  • V. M. Babich
  • D. B. Dement’ev
  • B. A. Samokish


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


Singular Point Integral Representation Asymptotic Formula Quadrature Formula Legendre Function 
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  1. 1.
    I. M. Ryzhik and I. S. Gradshtein, Tables of Integrals, Sums, Series, and Products [in Russian], Moscow (1951).Google Scholar
  2. 2.
    E. T. Whittaker and G. N. Watson, A Course of Modern Analysis [Russian translation], Moscow (1963).Google Scholar
  3. 3.
    B. A. Samokish, “A remark on the computation of definite integrals,” in: Methods of Computing, LGU (1963), pp.45–49.Google Scholar
  4. 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.MathSciNetGoogle Scholar
  5. 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).MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  • V. M. Babich
    • 1
  • D. B. Dement’ev
    • 2
  • B. A. Samokish
    • 2
  1. 1.St. Petersburg Department of the Steklov Mathematical InstituteSt. PetersburgRussia
  2. 2.St. Petersburg State UniversitySt. PetersburgRussia

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