高斯位移的雅可比第三θ函数求和
Summation of Gaussian shifts as Jacobi's third Theta function
摘要：
适当地选择Jacobi模恒等式（Jacobi虚变换）的参数意味着无限周期网格上的高斯位移之和可以表示为Jacobi第三θ函数。因此，高斯位移的求和和薛定谔方程的解之间的联系被明确地示出。利用高斯函数的形状参数，可以直接得到一个简洁的、可控的高斯位移和逼近常数函数的饱和误差上界.这阐明了如何选择形状参数，并提供了进一步的理解，使用高斯越来越平坦。
英文摘要：
A proper choice of parameters of the Jacobi modular identity (Jacobi Imaginary transformation) implies that the summation of Gaussian shifts on infinity periodic grids can be represented as the Jacobi's third Theta function. As such, connection between summation of Gaussian shifts and the solution to a Schrödinger equation is explicitly shown. A concise and controllable upper bound of the saturation error for approximating constant functions with summation of Gaussian shifts can be immediately obtained in terms of the underlying shape parameter of the Gaussian. This shed light on how to choose a shape parameter and provides further understanding on using Gaussians with increasingly flatness.
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