We proved the following proposition which is prepared to be used in the construction of approximate solutions to a differential equation in the field of Mikusiński operators. extsc{Proposition}. \emph{Let $(K,g)$ be a canonical element which satisfies the equation $(3)$, with its centre in the point $a\notin S_3$. We suppose that the radius $\rho$ of the circle $K$ is: $\rho=\min|z-a|$, $z\in S\cup S_3$, then for the Taylor series coefficients an of the canonical element $(K,g)$ we have}: \[ |a_n|eq\frac4{\rho n}e^2\Big(1-\frac2{n+k+1}\Big)^{k-1}(n+k)^{2m-1}|a_0|,\quad k\geq0,\quad n+k\geq4. \] The sets $S_1$, $S_2$, $S_3$ and $S$ are defined in the following way: $S_1\equiv\{z,P_n(z)=0\}$, $S_2\equiv\{z,D(z)=0\}$, $S_3\equiv\{z,p_0(z)=0\}$ and $S\equiv S_1\cup \S2$. $D(z)$ is the polynomial obtained from equations (2).