The Journal of the Indian Mathematical Society

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Special Value of the Hypergeometric Function 3F2 and Connection Formulae Among Asymptotic Expansions


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1 Department of Mathematics, Nagoya University, Chikusa-Ku, Nagoya-464, Japan
     

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The value 3F2 (α1, α2, α3 β1, β2 |1) of the hypergeometric function 3F2 (α1, α2, α3 β1, β2 |z) generally has no known elementary expression (see [02], [A5]). It satisfies holonomic linear difference equations in α1, α2, α3, β1, β2. In this note we determine the coefficients of associated connection formulae among all possible directions at the infinity. These are known to characterize it.
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  • Special Value of the Hypergeometric Function 3F2 and Connection Formulae Among Asymptotic Expansions

Abstract Views: 255  |  PDF Views: 1

Authors

K. Aomoto
Department of Mathematics, Nagoya University, Chikusa-Ku, Nagoya-464, Japan

Abstract


The value 3F2 (α1, α2, α3 β1, β2 |1) of the hypergeometric function 3F2 (α1, α2, α3 β1, β2 |z) generally has no known elementary expression (see [02], [A5]). It satisfies holonomic linear difference equations in α1, α2, α3, β1, β2. In this note we determine the coefficients of associated connection formulae among all possible directions at the infinity. These are known to characterize it.