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In this paper, we discuss the application of the author's $\tilde{d}^{(m)}$transformation to accelerate the convergence of infinite series$\sum^\infty_{n=1}a_n$ when the terms $a_n$ have asymptotic expansions that canbe expressed in the form $$a_n\sim(n!)^{s/m}\exp\left[\sum^{m}_{i=0}q_in^{i/m}\right]\sum^\infty_{i=0}w_in^{\gamma-i/m}\quad\text{as $n\to\infty$},\quad s\ \text{integer.}$$ We discussthe implementation of the $\tilde{d}^{(m)}$ transformation via the recursiveW-algorithm of the author. We show how to apply this transformation and how toassess in a reliable way the accuracies of the approximations it produces,whether the series converge or they diverge. We classify the different casesthat exhibit unique numerical stability issues in floating-point arithmetic. Weshow that the $\tilde{d}^{(m)}$ transformation can also be used efficiently toaccelerate the convergence of infinite products  $\prod^\infty_{n=1}(1+v_n)$, where  $v_n\sim \sum^\infty_{i=0}e_in^{-t/m-i/m}$ as $n\to\infty$,\ $t\geq m+1$ aninteger. Finally, we give several numerical examples that attest the highefficiency of the $\tilde{d}^{(m)}$ transformation for the different cases.

Acceleration of Convergence of Some Infinite Sequences  $\boldsymbol{\{A_n\}}$ Whose Asymptotic Expansions Involve Fractional Powers  of $\boldsymbol{n}$ via the $\tilde{d}^{(m)}$ transformation