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Proof of continued fraction identity of subfactorial

This is a particular case of a well know cfrac that can be found almost in any good textbook on continued fractions: $$ {}_1F_1(1;c+1;z)=\sum_{k=0}^\infty\frac{z^{k}}{(c+1)_k}\\ =\cfrac{c}{c-z\,+} …
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