  We show that certain hypergeometric series used to formulate mirror symmetry
for Calabi-Yau hypersurfaces, in string theory and algebraic geometry, satisfy
a number of interesting properties. Many of these properties are used in
separate papers to verify the BCOV prediction for the genus one Gromov-Witten
invariants of a quintic threefold and more generally to compute the genus one
Gromov-Witten invariants of any Calabi-Yau projective hypersurface.
