From Conformal Group to Symmetries of Hypergeometric Type Equations

Jan Dereziński ; Przemysław Majewski

Symmetry, integrability and geometry: methods and applications, Tome 12 (2016)

Résumé

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.

Détail

Keywords: Laplace equation; hypergeometric equation; confluent equation; Kummer's table; Lie algebra; conformal group.

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