\[\lim_{a\to\infty}{{}_{1}F_{1}}\left({a\atop\nu+\frac{1}{2}(m+1)};-a^{-1}%
\mathbf{T}\right)=\frac{A_{\nu}\left(\mathbf{T}\right)}{A_{\nu}\left(%
\boldsymbol{{0}}\right)}.\]