自然對數(natural exponential)

(1 - x^2) e^3x= (1 - x^2) ((3x)^0 / 0! + 3x/1! + (3x)^2 /2! + (3x)^3 /3! + ...)a(r) x^r = (3x)^r / r! - (x^2) [(3x) ^ (r - 2)] / (r - 2)! = [ (3x) ^ r - (r - 1) r (x^2) (3x) ^ (r - 2) ] / r!= [ (3x) ^ r - r (r - 1) (3^(r-2)) x^r) ] / r!= (x ^ r) [ 3 ^ r - r(r - 1) (3 ^ (r - 2)) ] / r!= (x ^ r) (3 ^ (r - 2)) [3^2 - r(r - 1)] / r!= (x ^ r) (3 ^ (r - 2)) (9 + r - r^2) / r!Soa(r) = (3 ^ (r - 2)) (9 + r - r^2) / r!