Geodesic
On some integral properties of modified Bessel functions
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 2, pp. 167-171.

Voir la notice de l'article provenant de la source Math-Net.Ru

New integral equaties for modified Bessel functions of an arbitrary complex order are presented. The properties of Lebedev–Skalskaya integral transforms are investigated. 
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J. M. Rappoport. On some integral properties of modified Bessel functions. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 2, pp. 167-171. http://geodesic.mathdoc.fr/item/ISU_2015_15_2_a5/

[1] Saitoh S., Integral Transforms, Reproducing Kernels and their Applications, Pitman Res. Notes in Math. Series, 369, Addison Wesley Longman Ltd., L., 1997, 280 pp. | MR

[2] Kilbas A. A., Saigo M., H-Transform. Theory and Applications, Chapman and Hall/CRC, Boca Raton, L.–N.Y.–Washington, D.C., 2004, 386 pp. | MR

[3] Lebedev N. N., Skalskaya I. P., “Some integral transforms related to Kontorovich–Lebedev transform”, Problems of mathematical physics, Nauka, L., 1976, 68–79 (in Russian)

[4] Lebedev N. N., Skalskaya I. P., “Dual integral equations connected with Kontorovich–Lebedev transform”, Appl. Math. Mech., 38:6 (1974), 1090–1097 (in Russian) | MR | Zbl

[5] Yakubovich S. B., Index Transforms, World Scientific Publishing, Singapore–New Jersey–L.–Hongkong, 1996, 248 pp. | MR | Zbl

[6] Poruchikov V. B., Rappoport J. M., “Inversion formulas for modified Kontorovich–Lebedev transforms”, Differ. Equations, 20:3 (1984), 542–546 (in Russian) | MR | Zbl

[7] Rappoport J. M., “Some properties of modified Kontorovich–Lebedev transforms”, Differ. Equations, 21:4 (1985), 724–727 (in Russian) | MR | Zbl

[8] Rappoport J. M., “Some results for modified Kontorovitch–Lebedev integral transforms”, Proceedings of the 7th International Colloquium on Finite or Infinite Dimensional Complex Analysis, Marcel Dekker Inc., 2000, 473–477 | MR | Zbl

[9] Rappoport J. M., “The properties, inequalities and numerical approximation of modified Bessel function”, Electronic Transactions on Numerical Analysis, 25 (2006), 454–466 | MR | Zbl

[10] Rappoport J. M., About modified Kontorovitch–Lebedev integral transforms and their kernels, Preprint 09P/001, Imperial College of Science, Technology and Medicine, Department of Mathematics, L., 2009, 31 pp.

[11] Rappoport J. M., “Some integral equations with modified Bessel function”, More Progresses in Analysis, Proceedings of the 5th ISAAC Congress, World Scientific Publishing, Singapore–New Jersey–L.–Hongkong, 2009, 269–278 | DOI | Zbl

[12] Yakubovich S. B., “Beurling's theorems and inversion formulas for certain index transforms”, Opuscula Mathematica, 29:1 (2009), 93–110 | MR | Zbl