02-150 Robert S. Maier

Transforming the Heun equation to the hypergeometric equation: I. Polynomial transformations (104K, LaTeX2e with SIAM macros) 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.

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