对于广义积分integral from n=0 to ∞ dm/dx^m(1/1+x^2)d^n/dx^n(1/1+x^2)dx和integral from n=0 to ∞ d^m/dx^m(sin x/x)d^n/dx^n(sin x/x)dx(m,n为非负整数),采用Fourier变换及级数计算出它们的值,并指出在区间(-∞,+∞)上可积的函...对于广义积分integral from n=0 to ∞ dm/dx^m(1/1+x^2)d^n/dx^n(1/1+x^2)dx和integral from n=0 to ∞ d^m/dx^m(sin x/x)d^n/dx^n(sin x/x)dx(m,n为非负整数),采用Fourier变换及级数计算出它们的值,并指出在区间(-∞,+∞)上可积的函数f(x),亦可仿此计算广义积分integral from n=0 to ∞ f^(m)(x)f^(n)(x)dx.展开更多
文摘对于广义积分integral from n=0 to ∞ dm/dx^m(1/1+x^2)d^n/dx^n(1/1+x^2)dx和integral from n=0 to ∞ d^m/dx^m(sin x/x)d^n/dx^n(sin x/x)dx(m,n为非负整数),采用Fourier变换及级数计算出它们的值,并指出在区间(-∞,+∞)上可积的函数f(x),亦可仿此计算广义积分integral from n=0 to ∞ f^(m)(x)f^(n)(x)dx.
