![_5F_4[1/2n+1,n,-x,-y,-z; 1/2n,x+n+1,y+n+1,z+n+1]
=(Gamma(x+n+1)Gamma(y+n+1)Gamma(z+n+1)Gamma(x+y+z+n+1))/(Gamma(n+1)Gamma(x+y+n+1)Gamma(y+z+n+1)Gamma(x+z+n+1)),](/images/equations/DougallsTheorem/NumberedEquation1.svg) |
是一个 
是 Bailey (1935, pp. 25-26) 将 Dougall-Ramanujan 恒等式 称为“Dougall 定理”。
Dougall 定理
另请参阅
Dougall-Ramanujan 恒等式, 广义超几何函数使用 Wolfram|Alpha 探索
参考文献
Bailey, W. N. Generalised Hypergeometric Series. Cambridge, England: Cambridge University Press, pp. 25-27, 1935.Dougall, J. "On Vandermonde's Theorem and Some More General Expansions." Proc. Edinburgh Math. Soc. 25, 114-132, 1907.Hardy, G. H. "A Chapter from Ramanujan's Note-Book." Proc. Cambridge Philos. Soc. 21, 492-503, 1923.Koepf, W. Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities. Braunschweig, Germany: Vieweg, p. 84, 1998.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, 1926.在 Wolfram|Alpha 中被引用
Dougall 定理请引用为
Weisstein, Eric W. “Dougall 定理。” 来自 MathWorld——Wolfram Web 资源。 https://mathworld.net.cn/DougallsTheorem.html