Some lower bounds for the quotients of normalized error function and their partial sums

The purpose of the present paper is to determine lower bounds for R Ekf(z) (Ekf)m(z) , R (Ekf)m(z) Ekf(z) , R n E 0 k f(z) (Ekf) 0m(z) o and R n (Ekf) 0m(z) E 0 k f(z) o , where Ekf is the generalized normalized error function of the form Ekf (z) = z + P? n=2 (?1)n?1 ((n?1)k+1)(n?1)! z n and (Ekf)m its partial sum. Furthermore, we give lower bounds for R I[Ekf](z) (I[Ekf])m(z) and R (I[Ekf])m(z) I[Ekf](z) , where I[Ekf] is the Alexander transform of Ekf. Several examples of the main results are also