  We discuss the amplitudes describing N-gluon scattering in type I superstring
theory, on a disk world-sheet. After reviewing the general structure of
amplitudes and the complications created by the presence of a large number of
vertices at the boundary, we focus on the most promising case of maximally
helicity violating (MHV) configurations because in this case, the zero Regge
slope limit (alpha' -> 0) is particularly simple. We obtain the full-fledged
MHV disk amplitudes for N=4,5 and N=6 gluons, expressed in terms of one, two
and six functions of kinematic invariants, respectively. These functions
represent certain boundary integrals - generalized Euler integrals - which for
N>= 6 correspond to multiple hypergeometric series (generalized Kampe de Feriet
functions). Their alpha'-expansions lead to Euler-Zagier sums. For arbitrary N,
we show that the leading string corrections to the Yang-Mills amplitude, of
order O(alpha'^2), originate from the well-known alpha'^2 Tr F^4 effective
interactions of four gauge field strength tensors. By using iteration based on
the soft gluon limit, we derive a simple formula valid to that order for
arbitrary N. We argue that such a procedure can be extended to all orders in
alpha'. If nature gracefully picked a sufficiently low string mass scale, our
results would be important for studying string effects in multi-jet production
at the Large Hadron Collider (LHC).
