Carlson is a Mathematica package that implements the symmetric elliptic integrals of B. C. Carlson.
Download the paclet from the releases page, and install it by evaluating the following in Mathematica:
Needs["PacletManager`"]
PacletInstall["/path/to/paclet/Carlson-1.0.paclet"]
where "/path/to/paclet/Carlson-1.0.paclet" should be replaced with the actual path to the downloaded paclet file.
See the file carlson.nb for more detailed information on the package.