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періодичних видань НАН України
From Conformal Group to Symmetries of Hypergeometric Type Equations
Репозиторій DSpace/Manakin
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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From Conformal Group to Symmetries of Hypergeometric Type Equations
Інший ID:
2010 Mathematics Subject Classification: 35J05; 33Cxx; 35B06
DOI:10.3842/SIGMA.2016.108
DOI:10.3842/SIGMA.2016.108
Посилання:
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.
Підтримка:
We thank Tom Koornwinder and anonymous referees for useful remarks. J.D. gratefully acknowledges
financial support of the National Science Center, Poland, under the grant UMO2014/15/B/ST1/00126.
Дата:
2016
Переглядів:
486
Завантажень:
283
Анотація:
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.
