The finite group of the Kummer solutions

Abstract

In this short communication, which is self-contained, we show that the set of 24 Kummer solutions of the classical hypergeometric differential equation has an elegant, simple group theoretic structure associated with the symmetries of a cube; or, in other words, that the underlying symmetry group is the symmetric group S ₄.

Keywords:

• Hypergeometric series
• Kummer solutions
• Symmetries of the cube

Acknowledgements

K. Srinivasa Rao wishes to thank Prof. N. Schamp and the Flemish Academic Center (VLAC), of the Royal Flemish Academy of Belgium for Science and the Arts, for a Fellowship (Oct.–Nov. 2002), during the final stages of preparation of this manuscript.