  The asymptotic expansions of the Wright functions of the second kind,
introduced by Mainardi [see Appendix F of his book {\it Fractional Calculus and
Waves in Linear Viscoelasticity}, (2010)], $$ F_\sigma(x)=\sum_{n=0}^\infty
\frac{(-x)^n}{n! \g(-n\sigma)}~,\quad M_\sigma(x)=\sum_{n=0}^\infty
\frac{(-x)^n}{n! \g(-n\sigma+1-\sigma)}\quad(0<\sigma<1)$$ for $x\to\pm\infty$
are presented. The situation corresponding to the limit $\sigma\to1^-$ is
considered, where $M_\sigma(x)$ approaches the Dirac delta function
$\delta(x-1)$. Numerical results are given to demonstrate the accuracy of the
expansions derived in the paper, together with graphical illustrations that
reveal the transition to a Dirac delta function as $\sigma\to 1^-$.
