Voir la notice de l'article provenant de la source Math-Net.Ru
@article{CHEB_2021_22_1_a16, author = {A. I. Nizhnikov and I. A. Shilin}, title = {On two formulas for {Macdonald} functions and their group-theoretical sense}, journal = {\v{C}eby\v{s}evskij sbornik}, pages = {225--233}, publisher = {mathdoc}, volume = {22}, number = {1}, year = {2021}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/CHEB_2021_22_1_a16/} }
TY - JOUR AU - A. I. Nizhnikov AU - I. A. Shilin TI - On two formulas for Macdonald functions and their group-theoretical sense JO - Čebyševskij sbornik PY - 2021 SP - 225 EP - 233 VL - 22 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/CHEB_2021_22_1_a16/ LA - ru ID - CHEB_2021_22_1_a16 ER -
A. I. Nizhnikov; I. A. Shilin. On two formulas for Macdonald functions and their group-theoretical sense. Čebyševskij sbornik, Tome 22 (2021) no. 1, pp. 225-233. http://geodesic.mathdoc.fr/item/CHEB_2021_22_1_a16/
[1] Vilenkin N. Ya., Spetsialnye funktsii i teoriya predstavlenii grupp, Nauka, M., 1965 | MR
[2] Vilenkin N. Ya., Shleinikova M. A., “Integralnye sootnosheniya dlya funktsii Uittekera i predstavleniya trekhmernoi gruppy Lorentsa”, Mat. sb., 81 (1970), 185–191 | Zbl
[3] Gelfand I. M., Graev M. I., Vilenkin N. Ya., Integralnaya geometriya i svyazannye s nei voprosy teorii predstavlenii, Fizmatlit, M., 1962 | MR
[4] Gradshtein I. S., Ryzhik I. M., Tablitsy integralov, summ, ryadov i proizvedenii, Fizmatlit, M., 1963 | MR
[5] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady. Dopolnitelnye glavy, Nauka, M., 1986 | MR
[6] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady. Spetsialnye funktsii, Nauka, M., 1983 | MR
[7] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady. Elementarnye funktsii, Nauka, M., 1981 | MR
[8] Shilin I. A., “Dvoinye $SO(2,1)$-invariantnye integraly i formuly dlya funktsii Uittekera”, Izvestiya vuzov. Matematika, 2012, no. 5, 56–66 | Zbl
[9] Aurich R., Lustig S., Steiner F., “Hyperbolic universes with a horned topology and the cosmic microwave background anisotropy”, Classical and Quantum Gravity, 21 (2004), 4901–4925 | DOI | MR | Zbl
[10] Bolte J., Steil G., Steiner F., “Arithmetical chaos and violation of universality in energy level statistics”, Physical Review Letters, 69 (1992), 2188–2191 | DOI | MR | Zbl
[11] Booker A. R., “A test for identifying Fourier coefficients of automorphic forms and applications to Kloosterman sums”, Experimental Mathematics, 9 (2000), 571–581 | DOI | MR | Zbl
[12] Bryson A. E., Control of spacecraft and aircraft, Princeton University Press, Princeton, 1994 | MR
[13] Heijhal D. A., The Selberg trace formula for ${\rm PSL}(2,\mathbb{R})$, Lecture Notes in Mathematics, 1001, Springer, Berlin, 1983 | DOI | MR
[14] Heijhal D. A., Rackner B. N., “On the topography of Maass vaveforms for ${\rm PSL}(2,\mathbb{Z})$”, Experimental Mathematics, 1 (1992), 275–305 | DOI | MR
[15] Gil A., Seguna J., Temme N. M., “Computation of the modified Bessel functions of the third kind of imaginary orders: uniform Airy-type asymptotic expansions”, Journal Computational and Applied Mathematics, 153 (2003), 225–234 | DOI | MR | Zbl
[16] Iwaniec H., Introduction to the spectral theory of automorphic forms, Revista Matematica Iberoamericana, Madrid, 1995 | MR | Zbl
[17] Shilin I. A., Junesang Choi, “Certain connections between the spherical and hyperbolic bases on the cone and formulas for related special functions”, Integral Transforms and Special Functions, 25:5 (2014), 374–383 | DOI | MR | Zbl
[18] Shilin I. A., Junesang Choi, “Some connections between the spherical and parabolic bases on the cone expressed in terms of the Macdonald functions”, Abstract and Applied Analysis, 2014, 741079 | MR | Zbl
[19] I. A. Shilin, J. Choi, J. W. Lee, “Some integrals involving Coulomb functions associated with the three-dimensional proper Lorentz group”, AIMS Mathematics, 5:6 (2020), 5664–5682 | DOI | MR | Zbl
[20] Shilin I. A., Nizhnikov A. I., “Some formulas for Legendre functions induced by the Poisson transform”, Acta Polytechnica, 51:1 (2011), 70–73
[21] Shilin I. A., Nizhnikov A. I., “Some formulas for Legendre functions related to the Poisson transform and Lorentz group representation”, Journal of Physics. Conference series, 356 (2012), 012020 | DOI
[22] Yakubivich S. V., Index transforms, World Scientific, Singapore, 1996 | MR
[23] Zhao P., “Quantum variance of Maass-Hecke cusp forms”, Communications in Mathematical Physics, 297 (2010), 475–514 | DOI | MR | Zbl