论文标题
雅各比公式的类比
Analogies of Jacobi's formula
论文作者
论文摘要
通过考虑具有参数$（a，b，c）的超几何差分方程的施瓦兹的地图，=（1/6,1/2,1）$或$（1/12,5/12,1）$，我们给出了Jacobi公式的一些类比$ \ vartheta_ {00}（τ）$和$λ（τ）$是theta常数，在上半平面上定义的lambda函数，而$ f（a，b，c; z; z）$是在单位磁盘上定义的超角度系列。作为我们公式的应用，我们提供了$ f（a，b，c; z）$的几个功能方程。
By considering Schwarz's map for the hypergeometric differential equation with parameters $(a,b,c)=(1/6,1/2,1)$ or $(1/12,5/12,1)$, we give some analogies of Jacobi's formula $\vartheta_{00}(τ)^2= F(1/2,1/2,1;λ(τ))$, where $\vartheta_{00}(τ)$ and $λ(τ)$ are the theta constant and the lambda function defined on the upper-half plane, and $F(a,b,c;z)$ is the hypergeometric series defined on the unit disk. As applications of our formulas, we give several functional equations for $F(a,b,c;z)$.
