Note on equivariant $I$-function of local $P^n$

Several properties of a hyepergeometric series related to Gromov-Witten theory of some Calabi-Yau geometries was studied in [8]. These properties play basic role in the study of higher genus Gromov-Witten theories. We extend the results of [8] to equivariant setting for the study of higher genus equivariant Gromov-Witten theories of some Calabi-Yau geometries.