  The six gluon disk amplitude is calculated in superstring theory. This
amplitude probes the gauge interactions with six external legs on Dp-branes, in
particular including e.g. F^6-terms. The full string S-matrix can be expressed
by six generalized multiple hypergeometric functions (triple hypergeometric
functions), which in the effective action play an important role in arranging
the higher order alpha' gauge interaction terms with six external legs (like
F^6, D^4 F^4, D^2 F^5, D^6 F^4, D^2 F^6, ...).
  A systematic and efficient method is found to calculate tree-level string
amplitudes by equating seemingly different expressions for one and the same
string S-matrix: Comparable to Riemann identities appearing in string-loop
calculations, we find an intriguing way of using world-sheet supersymmetry to
generate a system of non-trivial equations for string tree-level amplitudes.
These equations result in algebraic identities between different multiple
hypergeometric functions. Their (six-dimensional) solution gives the
ingredients of the string S-matrix. We derive material relevant for any open
string six-point scattering process: relations between triple hypergeometric
functions, their integral representations and their
alpha'-(momentum)-expansions given by (generalized) Euler-Zagier sums or
(related) Witten zeta-functions.
