Existence and uniqueness of the modified error function
  This article is devoted to prove the existence and uniqueness of solution to the non-linear second order differential problem through which is defined the modified error function introduced in Cho-Sunderland, J. Heat Transfer, 96-2:214-217, 1974. We prove here that there exists a unique non-negative analytic solution for small positive values of the parameter on which the problem depends. 
Andrea N. Ceretani, Natalia N. Salva and Domingo A. Tarzia
math.CA