一类n维椭球体上的n重积分及估计

A Class of n-Multiple Integral on the n-Dimensional Ellipsoid and Its Estimation

利用n维椭球坐标变换给出了定义在n维椭球体上的n重积分∫V(n∑i=1x_i^2)dx的结果,推广得到了更一般的n重积分∫Ωf(n∑i=1(x_i-a_i/b_i)~2)dx的结果及应用;并利用泰勒公式给出了一类多元函数重积分的估计.

In this paper,the n-dimension ellipsoid coordinate transformation is used to give the results of n-multiple integrals ∫V（n∑i=1x_i^2）dx which defined on the n-dimension ellipsoid, and the results and applica-tions of n-multiple integrals ∫Ωf（n∑i=1（x_i-a_i/b_i）^2）dx is generalized. Then the Taylor formula is used to esti-mate a class of multiple integrals of multivariate function.