I'm trying to understand this paper on blackholes https://articles.adsabs.harvard.edu/pdf/1979A%26A....75..228L
the following is in the paper: picture of equations However, I do not understand the syntax of the Jacobi elliptic function in (13). Do they not take 2 parameters, usually (u,m) Why is there only one parameter here, and why is it in curly brackets? Part of the parameter is an Elliptic integral of modulus k, would it be safe to assume the modulus of the Jacobi elliptic function is also k?
[Edit]
To clarify, the equation in the above image can be simplified for this posting to be:
$$1/r = g*(sn(a*γ + F(ζ, k))^2$$
My confusion is that from everything I've read about the Jacobi elliptic function sn, it takes 2 parameters, usually (u,m) but in this paper, they only have 1 parameter $(a*γ + F(ζ, k))$, in curly brackets (Which I couldn't get to show in the equation above so I'm using regular brackets). Is it fair to assume the author used k, from F(ζ, k), as the modulus for sn as well? Or is this some well-known syntax?