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Symmetry, Integrability and Geometry: Methods and Applications, 2016, Volume 12, 108, 69 pp.
DOI: https://doi.org/10.3842/SIGMA.2016.108
(Mi sigma1190)
 

From Conformal Group to Symmetries of Hypergeometric Type Equations

Jan Derezińskia, Przemysław Majewskiba

a Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warszawa, Poland
b Bureau of Air Defence and Anti-missile Defence Systems, PIT-RADWAR S.A., Poligonowa 30, 04-025 Warszawa, Poland
References:
Abstract: We show that properties of hypergeometric type equations become transparent if they are derived from appropriate 2nd order partial differential equations with constant coefficients. In particular, we deduce the symmetries of the hypergeometric and Gegenbauer equation from conformal symmetries of the 4- and 3-dimensional Laplace equation. We also derive the symmetries of the confluent and Hermite equation from the so-called Schrödinger symmetries of the heat equation in 2 and 1 dimension. Finally, we also describe how properties of the ${}_0F_1$ equation follow from the Helmholtz equation in 2 dimensions.
Keywords: Laplace equation; hypergeometric equation; confluent equation; Kummer's table; Lie algebra; conformal group.
Funding agency Grant number
National Science Centre (Narodowe Centrum Nauki) UMO-2014/15/B/ST1/00126
J.D. gratefully acknowledges financial support of the National Science Center, Poland, under the grant UMO-2014/15/B/ST1/00126.
Received: February 24, 2016; in final form October 20, 2016; Published online November 5, 2016
Bibliographic databases:
Document Type: Article
MSC: 35J05; 33Cxx; 35B06
Language: English
Citation: Jan Dereziński, Przemysław Majewski, “From Conformal Group to Symmetries of Hypergeometric Type Equations”, SIGMA, 12 (2016), 108, 69 pp.
Citation in format AMSBIB
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\by Jan~Derezi\'nski, Przemys\l aw~Majewski
\paper From Conformal Group to Symmetries of Hypergeometric Type Equations
\jour SIGMA
\yr 2016
\vol 12
\papernumber 108
\totalpages 69
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