论文标题
混合形态变换的复兴分析
Resurgence Analysis of Meromorphic Transforms
论文作者
论文摘要
我们考虑meromormormormormormormormormormormormormormormormormormormormormormormormormorphic Transform，并研究其在一定重新恢复下的渐近扩张。在衰减假设下，我们在这些变换的重新缩放参数中建立了完整的渐近扩展，并为误差项提供了全局估计。我们表明，由此产生的渐近系列是可重新定义的，我们为产生的复苏功能提供了公式，这使我们能够为Stokes系数提供公式。通过将这种Meromorormorthic变换应用于基本函数来获得许多经典功能，其中Faddeev量子差异，Euler Gamma函数，Riemann Zeta函数，高斯超角函数，而Gauss Zeta Zeta函数，并且是我们一般理论的极好例子。
We consider meromorphic transforms given by meromorphic kernels and study their asymptotic expansions under a certain rescaling. Under decay assumptions we establish the full asymptotic expansion in the rescaling parameter of these transforms and provide global estimates for error terms. We show that the resulting asymptotic series is Borel resummable and we provide formulae for the resulting resurgent function, which allows us to give formulae for the Stokes coefficients. A number of classical functions are obtained by applying such meromorphic transforms to elementary functions, of which, the Faddeev quantum dilogarithm, the Euler gamma function, the Riemann zeta function, the Gauss hypergeometric function and the Airy function are excellent examples of our general theory.
