e^(-x)的三次Hermite-Padé逼近系数多项式的递推公式

Recursive formulae of coefficient polynomials of cubic Hermite-Padé approximation to e^(-x)

利用e-x形如Pn(x)e-3x+Qm(x)e-x+Rs(x)=O(xn+m+s+2)的三次Hermite Pad啨逼近系数多项式Pn(x),Qm(x),Rs(x)的微分怛等式,得到这些多项式的递推公式.借助于这些递推公式,能够由Pn(x),Qm(x),Rs(x)计算出e-x的三次Hermite Pad啨逼近系数多项式Pn+1(x),Qm+1(x),Rs+1(x).最后给出数值例子.

By using of the differential identical relations of the coefficient polynomials of cubic Hermite-Padé (approximation) to e^(-x) with the form P_n(x)e^(-3x)+Q_m(x)e^(-x)+R_s(x)=O(x^(n+m+s+2)), the recursive formulae of coefficient polynomials P_n(x),Q_m(x),R_s(x) are obtained. Based on these recursive formulae,the coefficient polynomials P_(n+1)(x),Q_(m+1)(x),R_(s+1)(x) can be computed from the polynomials P_n(x),Q_m(x),R_s(x).Finally a numerical example is also given.