Geodesic
Quadrature formulas for singular integrals with weight functions
Vladikavkazskij matematičeskij žurnal, Tome 13 (2011) no. 2, pp. 56-62 
Sh. S. Khubezhty; L. Yu. Plieva; Z. V. Besaeva. Quadrature formulas for singular integrals with weight functions. Vladikavkazskij matematičeskij žurnal, Tome 13 (2011) no. 2, pp. 56-62. http://geodesic.mathdoc.fr/item/VMJ_2011_13_2_a5/
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     title = {Quadrature formulas for singular integrals with weight functions},
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Voir la notice de l'article provenant de la source Math-Net.Ru

We study singular integrals with weight functions and construct quadrature formulas for such integrals. Inversion formulas similar to the formulas for singular integrals with Chebyshev polynomials are proved. Application of obtained quadrature formulas to the numerical solution of singular integral equations are pointed out.

[1] Krylov V. I., Priblizhennye vychisleniya integralov, Nauka, M., 1967, 500 pp. | MR

[2] Krylov V. I., Shulgin L. T., Spravochnaya kniga po chislennomu integrirovaniyu, Nauka, M., 1966, 370 pp. | MR

[3] Ivanov V. V., Teoriya priblizhennykh metodov i ee primenenie k chislennomu resheniyu singulyarnykh integralnykh uravnenii, Naukova dumka, Kiev, 1968, 288 pp. | MR

[4] Lifanov I. K., Metod singulyarnykh integralnykh uravnenii i chislennyi eksperiment, TOO Yanus, M., 1995, 520 pp. | MR | Zbl

[5] Pashkovskii S., Vychislitelnye primeneniya mnogochlenov i ryadov Chebysheva, Nauka, M., 1983, 384 pp. | MR

[6] Panasyuk V. V., Savruk M. P., Datsyschin A. P., Raspredelenie napryazhenii okolo treschin v plastinakh i obolochkakh, Naukova dumka, Kiev, 1976, 444 pp. | MR

[7] Akhiezer N. I., “O nekotorykh formulakh obrascheniya singulyarnykh integralov”, Izv. AN SSSR. Matematika, 9:4 (1945), 275–290 | MR | Zbl

[8] Sege G., Ortogonalnye mnogochleny, Fizmatgiz, M., 1962, 500 pp.

[9] Pykhteev G. N., Tochnye metody vychisleniya integralov tipa Koshi, Nauka, Novosibirsk, 1980, 120 pp. | MR | Zbl

[10] Plieva L. Yu., Besaeva Z. V., “Ob odnoi kvadraturnoi formule i nekotore ee primenenie”, Tr. mezhdunar. simpoziuma (MDOZMF-2009), Kharkov–Kherson, 2009, 141–144