# Identity from Lectures on the Theory of Elliptic Functions by Harris Hancock

I'm working on Example $4$, page $262$, of Harris Hancock's book Lectures on the Theory of Elliptic Functions which reads:

Prove that $\dfrac{1}{\operatorname{sn}(iu,k)^2} + \dfrac{1}{\operatorname{sn}(u,k)^2} = 1$.

I can only get this result if $\operatorname{sn}(u,k) = \operatorname{sn}(u,k')$, where $k'$ is the complimentary modulus of $k$. But that does not make sense.

• You might want to specify what the function $\operatorname{sn}$ is. Jul 28, 2016 at 19:02
• It holds like this: $\dfrac{1}{\operatorname{sn}(iu,k)^2} + \dfrac{1}{\operatorname{sn}(u,k')^2} = 1$. There's probably a misprint in the book. Jul 28, 2016 at 19:34

$$\dfrac{1}{\operatorname{sn}(iu,k)^2} + \dfrac{1}{\operatorname{sn}(u,k')^2} = 1$$