Following function is important in applied mathematics and physics (probability theory and statistics, thermodynamics, etc.) and fits our present discussion.

Regarding it as a typical case of a special function defined by an integral that cannot be evaluated as in elementary calculus, do the following.

Obtain the Maclaurin series of erf x from that of the integrand. Use that series to compute a table of erf x for x = 0(0.01)3 (meaning x = 0, 0.01, 0.02, · · ·, 3).