论文标题
雅各比公式及其应用的类比
An analogy of Jacobi's formula and its applications
论文作者
论文摘要
我们给出了Jacobi公式的类比，该公式将超几何函数与参数$（1/4,1/4,1）$和Theta常数相关联。通过使用此类比和Theta常数的两次公式，我们获得了该超几何函数的转换公式。作为其应用，我们表达了由该超几何函数由平均迭代定义的两对序列的限制。
We give an analogy of Jacobi's formula, which relates the hypergeometric function with parameters $(1/4,1/4,1)$ and theta constants. By using this analogy and twice formulas of theta constants, we obtain a transformation formula for this hypergeometric function. As its application, we express the limit of a pair of sequences defined by a mean iteration by this hypergeometric function.
