Journal of the Ramanujan Mathematical Society

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Hypergeometric Functions for Function Fields II


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1 Department of Mathematics, University of Arizona, Tucson, AZ 85721, United States
     

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We develop the theory of hypergeometric functions introduced in [6] further by explaining the non-commutative and differential equations aspects and various analogies satisfied by it. In particular, we give analogue of Kummer's solutions at ∞, by defining a suitable analogue of  (α)-n. The analogies do not always work as expected naively.
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  • Hypergeometric Functions for Function Fields II

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Authors

Dinesh S. Thakur
Department of Mathematics, University of Arizona, Tucson, AZ 85721, United States

Abstract


We develop the theory of hypergeometric functions introduced in [6] further by explaining the non-commutative and differential equations aspects and various analogies satisfied by it. In particular, we give analogue of Kummer's solutions at ∞, by defining a suitable analogue of  (α)-n. The analogies do not always work as expected naively.