From Conformal Group to Symmetries of Hypergeometric Type Equations
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...
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| Date: | 2016 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2016
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/148546 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | From Conformal Group to Symmetries of Hypergeometric Type Equations / J. Dereziński, P. Majewski // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 48 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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 ₀F₁ equation follow from the Helmholtz equation in 2 dimensions. |
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