Special functions from quantum canonical transformations
arXiv:hep-th/9310168 · doi:10.1063/1.530725
Abstract
Quantum canonical transformations are used to derive the integral representations and Kummer solutions of the confluent hypergeometric and hypergeometric equations. Integral representations of the solutions of the non-periodic three body Toda equation are also found. The derivation of these representations motivate the form of a two-dimensional generalized hypergeometric equation which contains the non-periodic Toda equation as a special case and whose solutions may be obtained by quantum canonical transformation.
LaTeX, 24 pp., Imperial-TP-93-94-5 (revision: two sections added on the three-body Toda problem and a two-dimensional generalization of the hypergeometric equation)