The field $M$ of Mikusiński operators is the extension of the integral domain $\mathcal C$ [5]. In this paper, the two following basic problems are investigated in the field $M$. (a) The representation of a class of operators in the field $M$. (b) The continuity in the point of a class of operational functions in the sense of continuity in operational calculus [5]. As applications the following results were obtained. extsc{Lemma}. \emph{Let $\lambda\in R$, $0<v<1$, $\Phi(\alpha,-v;z)$ be the function of E.\,M. Wright and $_1F_1(n,n+1;z)$ be the confluent hypergeometric function. Then the following representation is valued} \begin{align*} \frac1{(s^v+ambda)^n}&=s\bigg\{\int_{0}^{ıfty}\Phi(0,-v;-xt^{-v})\frac{x^n}{n!}{}_1F_1(n,n+1;-ambda x)\frac{dx}{vx}\bigg\} &=s\bigg\{\int_{0}^{ıfty}\Phi(1,-v;-xt^{-v})\frac{x^{n-1}}{(n-1)!}e^{-ambda x}dx\bigg\}\quad(n=1,2,...) \end{align*} \emph{where s is a differential operator in $M$}. Let us consider the class of operational functions of the following form \begin{equation} Q_n(x)=\frac1{(lpha(x)S^v+\beta(x)^n}\quad nı N \end{equation} where $\alpha(x)$ and $\beta(x)$ are numerical continuous functions on the interval $I=[c,d]$ and $x_0\in I$, $\alpha(x_0)=0$, $\beta(x_0)\neq0$. extsc{Theorem}. \emph{The necessary and sufficient condition for the operational function $(1)$ to be continuous in the point $x=x_0$, is the existence of a neighbourhood $V_0(x_0)$ in which} \[ \gamma=\frac{\beta(x)}{lpha(x)}>0,extit{ while } xı V_0\backslash\{x_0\} \]