# Kappa function in infinite series

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.

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Did you see the little footnote at the end of your link, that next to the $K_{k=k_1}^{k_2}a_k/b_k$ has its definition? The $K$ is just shorthand for the continued-fraction operation, just as $\Sigma$ is shorthand for sum and $\Pi$ is for product. –  Andres Caicedo Apr 4 '11 at 23:56
thank you very much...i missed that –  tekknolagi Apr 5 '11 at 0:00
I guess $K$ comes from the Greek word κλάσμα=fraction. –  Pantelis Sopasakis Apr 5 '11 at 2:42
ooh that was helpful too - you're greek? awesome. –  tekknolagi Apr 5 '11 at 22:35
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.