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.
References
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).
N. Vasil'ev, J. Klokovs, and A. Skrstna,Applications of the Chebyshev Polynomials in Numerical Analysis [in Russian], Zinatne, Riga (1984).
J. Luke,Special Mathematical Functions and Their Approximations [Russian translation], Mir, Moscow (1980).
S. Paszkowski,Computation Applications of the Chebyshev Polynomials and Series [Russian translation], Nauka, Moscow (1983).
V. N. Belykh, “Calculation of some Cauchy-type integrals with a logarithmic singularity,”Dinamika Sploshn. Sredy, No. 40, 14–29, (1979).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhumal, Vol. 45, No. 8, pp. 1174–1176, August, 1993.
Rights and permissions
About this article
Cite this article
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
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01070981