![_7F_6[a,1+1/2a,b,c,d,e,-m; 1/2a,1+a-b,1+a-c, ; 1+a-d,1+a-e,1+a+m]
=((1+a)_m(1+a-d-e)_m)/((1+a-d)_m(1+a-e)_m)_4F_3[1+a-b-c,d,e,-m; 1+a-b,1+a-c,d+e-a-m]](/images/equations/WhipplesTransformation/NumberedEquation1.svg) |
(Bailey 1935, p. 25), 其中 
和 
是以 
为宗量的广义超几何函数，并且 
是伽玛函数。
惠普尔 (1926ab) 的另一个变换由下式给出
![_4F_3[a,b,-z,-n; u,v,w;1]
=(Gamma(u+z+n)Gamma(w+z+n)Gamma(v)Gamma(w))/(Gamma(v+z)Gamma(v+n)Gamma(w+n)Gamma(w+z))_4F_3[u-a,u-b,-z,-n; 1-v-z-n,1-w-z-n,u;1]](/images/equations/WhipplesTransformation/NumberedEquation2.svg) |
当 
或 
其中之一为非负整数时 (Andrews and Burge 1993)。
惠普尔变换
另请参阅
广义超几何函数, Watson-惠普尔变换, 惠普尔恒等式使用 Wolfram|Alpha 探索
参考文献
Andrews, G. E. and Burge, W. H. "Determinant Identities." Pacific J. Math. 158, 1-14, 1993.Bailey, W. N. Generalised Hypergeometric Series. Cambridge, England: Cambridge University Press, pp. 25 and 29, 1935.Whipple, F. J. W. "On Well-Poised Series, Generalized Hypergeometric Series Having Parameters in Pairs, Each Pair with the Same Sum." Proc. London Math. Soc. 24, 247-263, 1926a.Whipple, F. J. W. "Well-Poised Series and Other Generalized Hypergeometric Series." Proc. London Math. Soc. Ser. 2 25, 525-544, 1926b.Whipple, F. J. W. "A Fundamental Relation Between Generalized Hypergeometric Series." Proc. London Math. Soc. 26, 257-272, 1927.在 Wolfram|Alpha 中被引用
惠普尔变换引用为
Weisstein, Eric W. "惠普尔变换." 来自 MathWorld——Wolfram 网络资源. https://mathworld.net.cn/WhipplesTransformation.html