振荡函数的Hermite数值积分公式

The Formulas for Numerical Integral of Oscillating Functions

本文讨论了振荡函数形如∫１－１ｆ（ｘ）ｓｉｎωｘｄｘ，∫１－１ｆ（ｘ）ｃｏｓωｘｄｘ的Ｈｅｒｍｉｔｅ积分公式，它基于ｆ（ｘ）的Ｈｅｒｍｉｔｅ插值多项式的一些结论，导出了依赖于ｘｎｊ的ａｎｊ及不依赖于ｘｎｊ的ｇ（ｋ，ｗ）的权数因子的递推关系式，并给出误差分析．

A numerical integral problem as ∫ 1 -1 f(x) sin ωx d x , ∫ 1 -1 f(x) cos ωx d x is discussed in this paper, Some weight factors of recurrence relations as a nj and g(k,ω) are obtained by using some known results of Hermite interpolatory quadrature formulae. This method has some advantage without evaluating integrals of Hermite functions, and the error analysis is given.