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

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