I ran into this problem while studying the asymptotic behavior of a probability distribution function called tao2. It computes correctly at positive infinity but doesn't actually compute at negative infinity. Instead, Mathematica simply spits out the input. Is there any way to fix this?
tao2 = (2*(-(1/4)/E^(2*t^2)+Pi/8-((1/4)*Sqrt[Pi]*t)/E^t^2+(1/4)*Pi*Erf[t] -((1/4)*Sqrt[Pi]*t*Erf[t])/E^t^2+(1/8)*Pi*Erf[t]^2))/Pi
Update 1: Asymptotic works when I separate tau2 into two parts and compute separately (one contains all terms involving the error function, another contains all other terms). However, these two parts add up to 0, while I expect to see E^(-2*t^2)/t^2 times some constant.
Update 2: As Bob Hanlon suggested, the expanded form of the tao function is indeed more suitable for computation. However, when using both the original form and the expanded form on a tester function (called tao1), the two methods produce different results. Here
tao1 = (1/2)*(1+Erf[t])