Kummer恒等式的推广
A generalization of Kummer's identity
摘要：
当关系B-A+C=1成立时，著名的Kummer公式计算超几何级数2F 1（A，B;C;-1）.本文讨论了C-A+B为整数时2F 1（-1）级数的求值问题。这样的级数表示为两个Γ项的和乘以终止3F 2（1）级数。20世纪20年代惠普尔基本上已经知道了几个这样的公式。在这里，我们给出了一个更简单和更完整的概述这种类型的评估。此外，算法方面的评价超几何级数被认为是。我们举例说明Zeilberger的方法，并讨论其适用性的非终止系列，并提出了一对夫妇的其他已知公式类似的推广。
英文摘要：
The well-known Kummer's formula evaluates the hypergeometric series 2F1(A,B;C;-1) when the relation B-A+C=1 holds. This paper deals with evaluation of 2F1(-1) series in the case when C-A+B is an integer. Such a series is expressed as a sum of two Γ-terms multiplied by terminating 3F2(1) series. A few such formulas were essentially known to Whipple in 1920's. Here we give a simpler and more complete overview of this type of evaluations. Additionally, algorithmic aspects of evaluating hypergeometric series are considered. We illustrate Zeilberger's method and discuss its applicability to non-terminating series, and present a couple of similar generalizations of other known formulas.
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