All-order alpha-expansion of one-loop open-string integrals

We present a new method to evaluate the $alpha$-expansion of genus-one integrals over open-string punctures and unravel the structure of the elliptic multiple zeta values in its coefficients. This is done by obtaining a simple differential equation of Knizhnik-Zamolodchikov-Bernard-type satisfied by generating functions of such integrals, and solving it via Picard iteration. The initial condition involves the generating functions at the cusp $tauto iinfty$ and can be reduced to genus-zero integrals.