The finite group of the Kummer solutions

S. Lievens, K. Srinivasa Rao, J. Van Der Jeugt
2005 Integral transforms and special functions  
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 . Running head: On the Kummer solutions. E.E. Kummer [5] showed that the second order ordinary differential equation, characterized by three regular singular points at 0, 1
more » ... d ∞, i.e. with a, b and c real or complex parameters, has one solution as the hypergeometric series:
doi:10.1080/10652460410001672997 fatcat:dhozogcqyrgxvfajafhjio6ofy