$$1 + \cfrac{{\cfrac{1}{{1 \cdot s}}}}{{1 + \cfrac{{\cfrac{1}{{2 \cdot s}}}}{{1 + \cfrac{{\cfrac{1}{{3 \cdot s}}}}{{1 + ...}}}}}} = 1 + \cfrac{{1 + \cfrac{{1 + \cfrac{{1 + ...}}{{3s + 1}}}}{{2s + 1}}}}{{1s + 1}} = \sum\limits_{n = 0}^{ + \infty } {\frac{1}{{\prod\limits_{k = 1}^n {\left( {sk + 1} \right)} }}} = {s^{\frac{1}{s} - 1}}{e^{\frac{1}{s}}}\left( {\Gamma \left( {\frac{1}{s}} \right) - \Gamma \left( {\frac{1}{s},\frac{1}{s}} \right)} \right)$$