Proof of the Wilf–Zeilberger Conjecture for Mixed Hypergeometric Terms
Proof of the Wilf–Zeilberger Conjecture for Mixed Hypergeometric Terms
复制标题
混合超几何项的威尔夫·蔡尔伯格猜想的证明
DOI：
10.1016/j.jsc.2018.06.003
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发表时间：
2019
影响因子：
0.7
通讯作者：
ChristophKoutschan
中科院分区：
文献类型：
--
作者：
Shaoshi Chen;ChristophKoutschan
1992年，Wilf和Zeilberger证明了多个离散和连续变量的超几何项是完整的当且仅当它是真的。严格地说，这个猜想并不成立，但当它被适当地重新表述时，它是正确的：佩恩在1997年证明了一个分段解释，而阿布拉莫夫和佩特科夫舍克在2002年独立地证明了一个共轭解释。这两个结果解决了纯离散的情况下的猜想。在本文中，我们将他们的工作扩展到多个离散和连续变量的超几何项，并证明了Wilf-Zeilberger猜想在这种混合设置的共轭解释。
In 1992, Wilf and Zeilberger conjectured that a hypergeometric term in several discrete and continuous variables is holonomic if and only if it is proper. Strictly speaking the conjecture does not hold, but it is true when reformulated properly: Payne proved a piecewise interpretation in 1997, and independently, Abramov and Petkovšek in 2002 proved a conjugate interpretation. Both results address the pure discrete case of the conjecture. In this paper we extend their work to hypergeometric terms in several discrete and continuous variables and prove the conjugate interpretation of the Wilf–Zeilberger conjecture in this mixed setting.