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 nonperiodic 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 nonperiodic Toda equation as a special case and whose solutions may be obtained by quantum canonical transformation.
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