正交多项式及Pade逼近

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The Orthogonal Polynomials and the Pade’ Approximation

摘要: 利用Legendre多项式的性质,得到exp(x),tanx和tanhx简单形式的对角Pade逼近,在[-1,1]上P_n(x)对于任意较低次幂的多项式是正交的.在求得某些函数的分母时,利用了Gaus求积公式.
- 正交多项式 /
- Pade逼近 /
- Legendre多项式 /
- 数值逼近
Abstract: The diagonal Pade' approximates for exp(x).tan x and tanh x are obtained in a simple manner by using the property of Legendre polynomials that on [-1,1] P_n(x) is orthogonal to every polynomial of lower degree.Gauss's quadrature formula is used tofined the denomiators of some functions.
- orthogonal polynomials /
- Pade’ approximation /
- Legendrepolynomials /
- numerical approxiamtion

[1]	G.A.Baker,Jr.,Essentials of Pade' Approximants,Academic Press(1975).
[2]	W.B.Jones and W.J.Thron,Continued Fractions:Analytic Theory and Applications,Encyclopedia of Mathematics and its Applications Ⅱ,Addison Wesley Publ.Co.(1980).
[3]	E.B.Saff and R.S.Varga(Editors),Pade' and Rational Approximation,Academic Press(1977).