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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 741079, 8 pages
Some Connections between the Spherical and Parabolic Bases on the Cone Expressed in terms of the Macdonald Function
1Department of Mathematics, Sholokhov Moscow State University for the Humanities, Verkhnyaya Radishevskaya 16-18, Moscow 109240, Russia
2Department of Mathematical Modeling, Moscow Aviation Institute, Volokolamskoe Shosse 4, Moscow 125993, Russia
3Department of Mathematics, Dongguk University, Gyeongju 780-714, Republic of Korea
Received 7 November 2013; Accepted 26 December 2013; Published 11 February 2014
Academic Editor: Kwang Ho Shon
Copyright © 2014 I. A. Shilin and Junesang Choi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- I. A. Shilin and J. Choi, “Certain connections between the spherical and hyperbolic bases on the cone and formulas for related special functions,” Integral Transforms and Special Functions, 2013.
- I. A. Shilin, “SO(2, 1)-integrals and formulas for Whittaker functions,” Russian Mathematics, vol. 56, pp. 47–56, 2012.
- I. Shilin, “-invariant double integral transforms and formulas for the Whittaker functions,” Mathematica Balkanica, vol. 26, no. 1-2, pp. 241–256, 2012.
- I. A. Shilin and J. Choi, “Formulas for some cylinder functions associated with the group SO(2, 1),” submitted.
- N. J. Vilenkin, Special Functions and the Theory of Group Representations, AMS, Providence, RI, USA, 1968.
- E. D. Rainville, Special Functions, Macmillan Company, New York, NY, USA, 1960, Reprinted by Chelsea Publishing Company, Bronx, New York, NY, USA, 1971.
- A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 3: Special Functions, OPA (Overseas Publishers Association), Amsterdam B. V. Published under the License of Gordon and Breach Science Publishers, 1990.
- I. A. Shilin and A. I. Nizhnikov, “Some formulas for Legendre functions induced by the Poisson transform,” Acta Polytech, vol. 51, pp. 70–73, 2011.
- I. A. Shilin and A. I. Nizhnikov, “Some formulas for Legendre functions related to the Poisson transform and Lorentz group representation,” Journal of Physics: Conference Series, vol. 346, Article ID 012020, 2012.
- M. M. Rodrigues, N. Vieira, and S. Yakubovich, “A convolution operator related to the generalized Mehler-Fock and Kontorovich-Lebedev transforms,” Results in Mathematics, vol. 63, no. 1-2, pp. 511–528, 2013.
- S. B. Yakubovich, Index Transforms, World Scientific, 1996.
- H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science, Amsterdam, The Netherlands, 2012.
- Y. A. Brychkov, Handbook of Special Functions, CRC Press, Taylar & Francis Group, A Chapman & Hall Book, 2008.
- A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions, vol. 2, McGraw-Hill Book Company, New York, NY, USA, 1953..
- A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 2: Special Functions, OPA (Overseas Publishers Association), Amsterdam B. V. Published under the License of Gordon and Breach Science Publishers, 1986.
- I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, Academic Press, New York, NY, USA, 1980, Edited by A. Jeffrey, 6th edition, 2000.