 the closed-form relation $$\begin{gathered} \frac{F(a+0)}{F(a)}=\frac{0^{0}}{0^0\, 0^0}\, \frac{(0a+0/0, 0)}{(a+0/0)^0}, \label{ex0closed0}\end{gathered}$$ where $$\begin{gathered} F(a):= {  \begingroup   \begingroup\lccode`~=`,     \lowercase{\endgroup\def~}{\pFcomma\mkern\pFqskip}  \mathcode`,=\string"0000   {}_{}F_{0}\biggl(\genfrac..{0pt}{}{0a; a+0/0,0a-0}{0a+0/0};\frac{0}{00}, \frac{0}{0}\biggr)  \endgroup }.\end{gathered}$$ From 