A close approximation related to the error function

Abstract

The quantity fi(p) Ti(p) must be nonnegative, for otherwise we could choose (xi pi) so small that (5) could not hold. (We note here fni(x) > 0 for x E D by hypothesis.) A similar consideration in the case where pi > xi shows that fi(p)Ti(p) < 0. Hence fi(p) = T1(p). In the same manner one can show that ft(p) = Ti(p), i = 2, *.. , n. Thus Q*(x) and T(x) are identical. The idea for this note occurred to the author after hearing a lecture by Prof. Ranko Bojanic [1] on best one sided approximation in the case of functions of one variable.