From Conformal Group to Symmetries of Hypergeometric Type Equations

Symmetry Integrability and Geometry-Methods and Applications

article

Jan Dereziński¹  Przemysław Majewski² 

[1] Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw;Bureau of Air Defence and Anti-missile Defence Systems

关键词: Laplace equation;    hypergeometric equation;    confluent equation;    Kummer’s table;    Lie algebra;    conformal group;   

DOI  :  10.3842/SIGMA.2016.108

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown