15.8 Let errf(x) denote the regular error functions, that is, errf(x) = 2 x 0 et2 dt. Show that erf(x)=1 ex2

15.8 Let errf(x) denote the regular error functions, that is, errf(x) = 2

√π

 x 0

e−t2 dt.

Show that erf(x)=1 − e−x2

√π

! 1 x − 1 2x3 + ... "

.

Furthermore, show that limε→0 2

ε

!

1 − Φ

! δ

σ

√ε

"" = 0 for all σ > 0 and δ > 0. Here, φ(x) denotes the cdf of a N(0, 1) random variable.