An Apery-like Difference Equation for Catalan's Constant
An Apery-like Difference Equation for Catalan's Constant
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DOI：
10.37236/1707
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发表时间：
2002-01
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影响因子：
--
通讯作者：
W. Zudilin
中科院分区：
文献类型：
--
作者：
W. Zudilin
将Zeilberger的创造性伸缩算法应用于一类含有有理分量的Catalan常数中线性形式的非常稳定的超几何级数，得到了这些形式及其分量的二阶差分方程。由此，我们得到了一种快速计算加泰罗尼亚常数的新方法，以及它的一个新的连分式展开式。对于(4)=4/90的二阶微分方程式和新的连分式，也提出了类似的论点。
Applying Zeilberger’s algorithm of creative telescoping to a family of certain very-well-poised hypergeometric series involving linear forms in Catalan’s constant with rational coecients, we obtain a second-order dierence equation for these forms and their coecients. As a consequence we derive a new way of fast calculation of Catalan’s constant as well as a new continued-fraction expansion for it. Similar arguments are put forward to deduce a second-order dierence equation and a new continued fraction for (4) = 4 /90.