Kappa function in infinite series

Question

I saw a greek letter in an infinite series, and found out it was Kappa. What does this do? It looks like a giant K.

http://www.wolframalpha.com/input/?i=find+continued+fraction+of+square+root

That's where i found it.

Answer 1

This is the notation for a Generalized Continued Fraction. $$ \mathrm{K}_{k=0}^n \frac{a_k}{b_k} = \frac{a_0}{b_0 + \frac{a_1}{b_1 + \frac{a_2}{b_2 + \ddots}}}$$

See that? The numerators in the $K$ notation, in this case $a_k$, denotes the numerators on each branch of a continued fraction. The denominator in the $K$ notation, in this case $b_k$, denotes the addend adjacent to the the next iteration of the fraction.

I hope that makes sense to you and helps. Unfortunately I could not figure out how to make a capital Kappa Κ in latex.