Algebraic Analysis of Exponential Asymptotics

2-对Dufling equation的参数表达式不对称解决方案是通过使用多尺度分析来构建的。这就证明了与四分之一的雅各比的椭圆功能条款中编写的解决方案的扩展和硬币，从而证明了正式解决方案的融合和硬币。第二个斯托克斯的几何图形和第三个痛苦的形状是确定的。Ansatz讨论了与较大参数一起使用的第三顺序正常差异相等的斯托克斯比值确定性。在解决方案有整体表示的情况下，通过使用最陡峭的下降路径的方法检测到的斯托克斯几何形状是一致的。一个度量的一个局部环的有限子集的一个度量的转录。这证明了这一标准是有限的，因为正式功率系列戒指中的某些家族的特殊功能。加布里埃尔洛夫的理论对正式功能的扩展是可用的。不同的操作员在p-valent meromorphic函数空间中发挥作用，并在p-valent meromorphic函数家族中引入了一些不同的指标，并使用了它们。由于单元磁盘上的分析功能，即原始的消失和衍生物是固有的，扭曲的不质，其中包含Ruscheweyh衍生物被发现。

・2-paramnetered exponential asymptotic solution to the Dufling equation is constructed by using the multiple-scale analysis. It is proved that the formal solution converges and coincides with the ・Fourier series expansion of the solution written in terms of Jacobi's elliptic function obtained by quadrature.・The Stokes geometry of the second and the third Painleve equations are determined.・An Ansatz concerning determination of Stokes gepmetry of third order ordinary differential equations with a large parameter is proposed. In the case where the solutions have integral representations, the Stokes geometries obtained by the Ansatz are consistent with the Stokes phenomen detected by using the method of the steepest descent paths.・A measure which measures transcendence of a finite subset of a local ring. It is proved that the measure is finite for some family of special functions in the formal power series ring.・An extension of Gabrielov's theorem to the formal functions is obtained.・A differential operator acting on the space of p-valent meromorphic functions is introduced and some differential inequalities for the family of p-valent meromorphic functions are obtained by using them.・For analytic functions on the unit disk that vanish on the origin and the derivative there is identical, distortion inequalities that contains Ruscheweyh derivatives are obtained.