 02150 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.
Heuntohypergeometric transformations are analogous to the classical
hypergeometric identities (i.e., hypergeometrictohypergeometric
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 higherdegree transformations.
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