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Values of Gaussian hypergeometric series and their connections to algebraic curves

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In this paper, we explicitly evaluate certain special values of 2F1 hypergeometric series. These evaluations are based on some summation transformation formulas of Gaussian hypergeometric series. We find expressions of… Click to show full abstract

In this paper, we explicitly evaluate certain special values of 2F1 hypergeometric series. These evaluations are based on some summation transformation formulas of Gaussian hypergeometric series. We find expressions of the number of points on certain algebraic curves over ????q in terms of Gaussian hypergeometric series, which play the vital role in deducing the transformation results.

Keywords: values gaussian; series connections; series; algebraic curves; hypergeometric series; gaussian hypergeometric

Journal Title: International Journal of Number Theory
Year Published: 2018

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