On addition theorems related to elliptic integrals

This paper provides some explicit formulas related to addition theorems for elliptic integrals ${\int }_0^{x}dt\mathrm{/}R(t)$, where $R(t)$ is the square root from a polynomial of degree 4. These integrals are related to complex elliptic genera and are motivated by Euler’s addition theorem for elliptic integrals of the first kind.