\lim_{{b\to-n}}\frac{\mathop{M\/}\nolimits\!\left(a,b,z\right)}{\mathop{\Gamma% \/}\nolimits\!\left(b\right)}=\mathop{{\mathbf{M}}\/}\nolimits\!\left(a,-n,z% \right)=\frac{\left(a\right)_{{n+1}}}{(n+1)!}z^{{n+1}}\mathop{M\/}\nolimits\!% \left(a+n+1,n+2,z\right).
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