On addition theorems related to elliptic integrals

preprint2019arXivOpen access

Abstract

This paper provides some explicit formulas related to addition theorems for elliptic integrals ∫0xdt/R(t)\int_0^x dt/R(t), where R(t)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.

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