e^(-x)的二次Padé逼近多项式的递推公式

Recurring formula of quadratic Padé approximation′s polynomials of e^(-x)

指数函数是非常重要的初等函数 ,它在微分方程中有特殊的作用 ,关于指数函数的二次 Padé逼近的文献已有许多 ,但是关于指数函数的二次 Padé逼近多项式的递推公式的文献 ,至今还没有看到。该文首先证明指数函数的二次 Padé逼近多项式的一组微分恒等式 ,然后由这一组微分恒等式得到指数函数的二次 Padé逼近多项式的递推公式 ,利用所给出的递推公式 ,就能够由指数函数的 (m ,n,r)型二次 Padé逼近多项式计算出它的 (m + 1,n + 1,r+ 1)型二次 Padé逼近多项式。最后给出数值例子。

The exponential function is a very important elementary function,and it is specially used in differential equation.There have been a lot of papers about the exponential function′s quadratic Padé approximation, but the papers has not been seen about recurring formula of the quadratic Padé approximation′s polynomials of the exponential function. In this paper, a group of differential identity expressions of the quadratic Padé approximation′s polynomials of the exponential function is firstly testified , then the recurring formula of the quadratic Padé approximation′s polynomials of the exponential function is obtained by using this group differential identity expressions.The (m+1,n+1,r+1) type quadratic Padé approximation′s polynomials of e -x are computed from its (m,n,r) type quadratic Padé approximation′s polynomials by using this recurring formula. A numerical example is also given.