On Well-Poised Series, Generalized Hypergeometric Series having Parameters in Pairs, each Pair with the Same Sum
On Well-Poised Series, Generalized Hypergeometric Series having Parameters in Pairs, each Pair with the Same Sum
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DOI：
10.1112/plms/s2-24.1.247
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发表时间：
--
影响因子：
1.8
通讯作者：
F. Whipple
中科院分区：
文献类型：
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作者：
F. Whipple
在§§ 2-8中，讨论了一个平衡级数的和既可以用有限项表示，也可以表示为一个低阶超几何级数的和的情况。在§§ 10-14中，讨论了这样的超几何级数本身可以求和的一些特殊情况，因此，平衡级数也可以求和。在§§ 15，16中，我们展示了如何通过颠倒公式和用平衡级数表示其他超几何级数来建立重要的一般命题。
In §§ 2-8 the cases in which the sum of a well-poised series can either be expressed in finite terms or as the sum of a hypergeometric series of lower order are discussed. In §§ 10-14 some of the special cases in which such hypergeometric series can themselves be summed, so that the well-poised series can also be summed, are dealt with. In §§ 15, 16 it is shown how important general propositions can be established by reversing the formulae and expressing other hypergeometric series in terms of well-poised series.