The two are related because erf(x) is the integral of exp(-t^2) from 0 to x. So this is correct if you interpret coefficients in the basis {x^n/n!} and drop the

The two are related because erf(x) is the integral of exp(-t^2) from 0 to x. So this is correct if you interpret coefficients in the basis {x^n/n!} and drop the scaling factor of 2/sqrt(pi). The Taylor series of exp has a 1 in the zeroth coefficient, so integrating from 0 to x we get a 1 in the 1st coefficient of erf. exp(-x^2) = 1 - x^2 + x^4/2 - x^6/6 + ... = 1/0! - 2x^2/2! + 12x^4/4! - 120x^6/6! + ... erf(x) = x/1! - 2x^3/3! + 12x^5/5! - 120x^7/7! + ...