The Abel summation of the Kontorovich-Lebedev integral representation

• Autorzy: Cojuhari P.A. , Gomilko A.M.
• Języki publikacji: EN

Abstrakty

EN

A new result on the summation of the Kontorovich-Lebedev integral representation in the sense of Abel mean is given.

Słowa kluczowe

EN

integral transforms; transforms of special functions; special functions; operational calculus; Kontorovich-Lebedev

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2005
• Tom: Vol. 25, no. 1
• Strony: 101--107
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Cojuhari P.A.

• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland

autor

Gomilko A.M.

• National University of Trade and Economics Department of Higher and Applied Mathematics Kiev, Ukraine

Bibliografia

• [1] Brychkov Yu. A., Marichev O.I., Prudnikov A. P.: Integral and series. Vol. 1. Moscow, Nauka 1981, 800 (Russian).
• [2] Gomilko A.M.: The Kontorovich-Lebedev integral transform. Ukrainskii Matematicheskii Zhurnal. 43 (1991) 10, 1259-1261 (Russian). English transl.: Ukra­inian Mathematical Journal, 1992, 1259-1263.
• [3] Grinchenko V. T., Ulitko A. F.: Three-dimensional Problems of the Theory of Ela­sticity. Vol. 3, Equilibrium of Elastic Bodies of Canonical Form. Kiev, Naukova dumka 1985, 280 (Russian).
• [4] Kontorovich M.I., Lebedev N.N.: On a method of solving certain problems of diffraction theory and related problems. Zh. Eksp. Teor. Fiz. 8 (1938) 10-11, 1192-1206 (Russian).
• [5] Lebedev N.N.: On an inversion formula. DAN 52 (1946), 395-398 (Russian).
• [6] Lebedev N.N.: On the representation of an arbitrary function by an integral involving cylinder functions of imaginary index and argument. Prikl. Matem. Mekh. 13 (1949) 5, 465-476 (Russian).
• [7] Lebedev N.N.: Special Functions and Applications. Moscow-Leningrad, Nauka 1963, 360 (Russian).
• [8] Titchmarsh E. C.: Introduction to the Theory of Fourier Integrals. Oxford, 1937.
• [9] Uflyand Ya. S.: Integral Transforms in Problems of Elasticity Theory. Leningrad, Nauka 1967, 404 (Russian).
• [10] Vu Kim Tuan, Yakubovich S.B.: The Kontorovich-Lebedev integral transform in a new class of Functions. Doklady Akad. Nauk Bel. SSR 29 (1985) 1, 11-14 (Russian).