Question

请高手计算一个无穷级数的和,F(x)=x/(1×1!)+x^2/(3×2!)+x^3/(5×3!)+x^4/(7×4!)

Answer 1

F(x)=(n=1～∞)∑x^n/[(2n-1)×n!]

x^(-0.5)*F(x)=(n=1～∞)∑x^(n-0.5)/[(2n-1)×n!]

[x^(-0.5)*F(x)]'=(n=1～∞)∑{x^(n-0.5)/[(2n-1)×n!]}'=(n=1～∞)0.5∑{x^(n-1.5)/n!}=x^(-1.5)∑x^n/n!=x^(-1.5)*[e^x-1]

∫[x^(-0.5)*F(x)]'dx=∫x^(-1.5)*(e^x-1)dx

F(x)=x^(+0.5)*∫x^(-1.5)*(e^x-1)dx

下面积分我就不会了,望有高手解决