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On the calculation of certain singular integrals

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Ukrainian Mathematical Journal Aims and scope

Abstract

A method for the approximate calculation of Cauchy-type integrals with logarithmic singularities is proposed. It is based on the expansion of a functionf(t) in a series in the Chebyshev polynomials.

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References

  1. N. V. Kulich, “On the calculation of some Cauchy-type integrals and singular integrals with logarithmic singularities,”Izv. Akad. Nauk Belorus. SSR, Ser. Fiz.-Mat., No. 1, 90–94 (1974).

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  2. N. Vasil'ev, J. Klokovs, and A. Skrstna,Applications of the Chebyshev Polynomials in Numerical Analysis [in Russian], Zinatne, Riga (1984).

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  3. J. Luke,Special Mathematical Functions and Their Approximations [Russian translation], Mir, Moscow (1980).

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  4. S. Paszkowski,Computation Applications of the Chebyshev Polynomials and Series [Russian translation], Nauka, Moscow (1983).

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  5. V. N. Belykh, “Calculation of some Cauchy-type integrals with a logarithmic singularity,”Dinamika Sploshn. Sredy, No. 40, 14–29, (1979).

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Authors and Affiliations

  1. Cherkassy Institute of Technical Engineering, Cherkassy

    A. I. Litvin & I. L. Kovalenko

  2. Omsk Pedagogical Institute, Omsk

    S. D. Simonzhenkov

Authors
  1. A. I. Litvin
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  2. S. D. Simonzhenkov
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  3. I. L. Kovalenko
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Additional information

Translated from Ukrainskii Matematicheskii Zhumal, Vol. 45, No. 8, pp. 1174–1176, August, 1993.

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Litvin, A.I., Simonzhenkov, S.D. & Kovalenko, I.L. On the calculation of certain singular integrals. Ukr Math J 45, 1312–1315 (1993). https://doi.org/10.1007/BF01070981

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  • DOI: https://doi.org/10.1007/BF01070981

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