Infinite Continued Fraction Notation

Wikipedia cites a notation by Gauss: $$ x = a_0 + \dfrac{1}{a_1 + \dfrac{1}{a_2 + \dfrac{1}{a_3}}} $$ would be written: $$ x = a_0 + \mathop{\mathrm{K}}_{k = 1}^3 \frac{1}{a_k} $$