  We study the D3-brane moduli dependence of the non-perturbative
superpotential generated by the D7-brane gaugino condensation in a type IIB
compactification on an orientifold of the elliptic Calabi-Yau threefold
$\Bbb{P}_{[1,1,1,6,9]}[18].$ Building on the work of Ganor, in the weak
coupling limit, we compute the D3-brane dependent one-loop pfaffian in the flat
coordinates and find that the one-loop pfaffian is written as the Jacobi theta
function. We also comment on the complex structure dependence of the D3-brane
dependent one-loop pfaffian.
