# Weird large K symbol

Take a look at this symbol:

$$\pi=3 + \underset{k=1}{\overset{\infty}{\large{\mathrm K}}} \frac{(2k-1)^2} 6$$

It is the notation for a continued fraction. In general: $$b_0 + \underset{k=1}{\overset{\infty}{\large{\mathrm K}}} \left(\frac{a_k}{b_k}\right)=b_0 + \cfrac{a_1}{b_1 + \cfrac{a_2}{b_2 + \cfrac{a_3}{b_3 + \cfrac{a_4}{b_4 + \ddots\,}}}}$$ Therefore, the continued fraction representation you have written above for $\pi$ is: $$\pi=3 + \underset{k=1}{\overset{\infty}{\large{\mathrm K}}} \frac{(2k-1)^2}{6}=3 + \cfrac{1^2}{6 + \cfrac{3^2}{6 + \cfrac{5^2}{6 + \cfrac{7^2}{6 + \ddots\,}}}}$$ A proof of this result can be found on pages 399-401 of this document by Paul Loya.
• An interesting aspect of this notation is that the apparent sequence of fractions $\frac {a_k_} {b_k_}$ is not actually used. Given that, I find this notation rather unfortunate. Mar 10, 2017 at 9:05