On Addition Theorems Related to Elliptic Integrals

Resumo

We present formulas for the components of the Buchstaber formal group law and its exponent over ℚ[p₁, p₂, p₃, p₄]. This leads to an addition theorem for the general elliptic integral \(\int_0^x {dt{\rm{/}}R\left( t \right)} \) with \(R(t)=\sqrt{1+p_{1} t+p_{2} t^{2}+p_{3} t^{3}+p_{4} t^{4}}\). The study is motivated by Euler’s addition theorem for elliptic integrals of the first kind.