非均匀复变函数的级数理论

Series Theory of Heterogeneous Complex Variable Function

本文把复变函数的级数理论推广到非均匀复变函数上,运用非均匀解析函数理论建立了非均匀幂级数的收敛域和收敛椭圆半径,同时利用非均匀Cauchy积分公式和Cauchy积分的高界导数公式建立了非均匀解析函数的泰勒定理。

In this paper, the series theory of complex variable function is applied to heterogeneous complex variable function. The convergence region and the radius of convergence ellipse of heterogeneous power series are established by using the theory of heterogeneous analytic function. At the same time, the Taylor’s theorem of heterogeneous analytic function is established by using the hetero-geneous Cauchy integral formula and the high order derivative formula of Cauchy integral.