Research in the Mathematical Sciences ( IF 1.2 ) Pub Date : 2021-04-28 , DOI: 10.1007/s40687-021-00266-3 Mohit Tripathi , Rupam Barman
In this article, we find finite field analogues of certain identities satisfied by the classical \({_4}F_3\)-hypergeometric series and Appell series. As an application, we find new summation and product formulas satisfied by the Gaussian hypergeometric series. For example, we express a \({_4}F_3\)-Gaussian hypergeometric series as a sum of two \({_2}F_1\)-Gaussian hypergeometric series. We also find two identities expressing \({_4}F_3\)-Gaussian hypergeometric series as a product of two \({_2}F_1\)-Gaussian hypergeometric series. As another application, we find a special value of a \({_4}F_3\)-Gaussian hypergeometric series using the summation formula.
中文翻译:
有限域上的Appell级数和高斯超几何级数
在本文中,我们找到了经典\({_ 4} F_3 \)-超几何级数和Appell级数满足的某些恒等式的有限域类似物。作为一种应用,我们找到了高斯超几何级数满足的新求和和乘积公式。例如,我们将\({_ 4} F_3 \)-高斯超几何级数表示为两个\({_ 2} F_1 \)-高斯超几何级数的总和。我们还找到了两个表示\({_ 4} F_3 \)-高斯超几何级数的恒等式,作为两个\({_ 2} F_1 \)-高斯超几何级数的乘积。作为另一个应用程序,我们使用求和公式找到\({_ 4} F_3 \)-高斯超几何级数的特殊值。