e^(-x)的三次Hermite-Padé逼近多项式的惟一性与微分恒等式  

Unicity and differential identity of triple Hermite-Padé approximation's polynomials of e^(-x)

作　　者：郭清伟[1] 

机构地区：[1]合肥工业大学理学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2002年第6期1214-1217,共4页Journal of Hefei University of Technology：Natural Science

摘　　要：首先证明了一个关于指数函数恒等式的指数不等式;根据这个指数不等式得到了在首项系数为1的条件下,指数函数e-x的三次Hermite-Padé逼近多项式的惟一性;最后根据指数函数e-x的三次Hermite-Padé逼近多项式的惟一性,得到了指数函数e-x的(k,l,m,n)型三次Hermite-Padé逼近多项式与(k-1,l-1,m-1,n-1)型三次Hermite-Padé逼近多项式之间的一组微分恒等式。In this paper,an exponential inequality about the exponential function equality is verified firstly. Then the unicity of the triple HermitePadé approximation's polynomials of the exponential function e-x is obtained by the exponential inequality under the condition that the highest coefficient of an approximation's polynomial should be one. Finally a group of differential identity is gotten about the (k,l,m,n) type triple HermitePadé approximation's polynomials of the exponential function e-x and its (k-1,l-1,m-1,n-1) type triple HermitePadé approximation's polynomials.

关 键 词：e^-x 三次Hermite-Padé逼近多项式 惟一性 微分恒等式 指数函数 微方程 

分 类 号：O241.5[理学—计算数学] O241.[理学—数学]