Wangerin函数S_m^n(μ)的数值计算及数值可视化分析

RESEARCH ON THE NUMERICAL CALCULATION OF WANGERIN FUNCTION S_m^n(μ) AND ITS NUMERICAL VISUALIZATION ANALYSIS

结合第一类完全椭圆积分的迭代算法和Jacobi椭圆函数的恒等式,实现Wangerin函数S_m^n(μ)的高精度数值计算.进一步,利用数值可视化方法对它的数值计算结果进行分析,总结出Wangerin函数S_m^n(μ)的曲线变化特征.这为深入研究Wangerin函数的收敛性和稳定性奠定理论基础,具有一定的工程实际价值.

Based on the iterative algorithm of complete elliptic integral of the first kind and identical equations of Jacobi elliptic functions, the high-precision numerical solutions of Wangerin function S^nm,（μ） are achieved. Furthermore, use numerical visualization method to take numerical analysis on its numerical calculation results, and to draw a conclusion on the variation characteristics of Wangerin function S^nm,（μ） curve. This study will provide theoretical basis for the further study on the convergence and stability of Wangerin function, which is of certain practical value in engineering.