- 02-150 Robert S. Maier
- Transforming the Heun equation to the hypergeometric equation: I. Polynomial transformations
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Mar 26, 02
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Abstract. The reductions of the Heun equation to the hypergeometric equation by
rational changes of its independent variable are classified.
Heun-to-hypergeometric transformations are analogous to the classical
hypergeometric identities (i.e., hypergeometric-to-hypergeometric
transformations) of Goursat. However, a transformation is possible only if
the singular point location parameter and normalized accessory parameter of
the Heun equation are each restricted to take values in a discrete set.
The possible changes of variable are all polynomial. They include
quadratic and cubic transformations, which may be performed only if the
singular points of the Heun equation form a harmonic or an equianharmonic
quadruple, respectively; and several higher-degree transformations.