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已知幂級數e^x =∑(n>=0)(x^n)/n!,x∈R, 因此 f(x)=(1+x^2)*(e^x) =(1+x^2)*∑(n>=0)(x^n)/n! =∑(n>=0)(x^n)/n!+(x^2)*∑(n>=0)(x^n)/n! =∑(n>=0)(x^n)/n!+∑(n>=0)[x^(n+2)]/n! =……,x∈R, 即為所求.
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