广义Cauchy中值定理中值点的渐近性态及仿真

The Asymptotic Behavior of Mid-value Point for Generalized Cauchy Mean Value Theorem and Simulation

利用Γ函数和B函数等工具对广义Cauchy中值定理的中值点ξ的渐近性进行研究,得到了若干新的渐近性理论成果,同时利用MATLAB和GeoGebra软件对此理论成果进行了仿真研究,其可视化结果明确了中值ξ(x)的单值、多值和收敛速度等多种性态.

The asymptotic behavior of mid-value point ξ(x) for generalized Cauchy mean value theorem is studied in this paper.By using Beta function and Gamma function,we give some new asymptotic behavior theory results.Then,We use MATLAB Simulation software and GeoGebra software to simulate the theoretical results.The result clearly visualize the ξ(x) are one-valued or multiple-valued and the asymptotic convergence rate and so on.