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In this paper, the generalized polylogarithm Φ _{p, q} (a, b, z), which is a particular representation of generalized hypergeometric functions, is considered. Conditions on the parameters a, b, p and q are found such that the normalized form of these generalized polylogarithms has certain geometric properties such as close-to-convexity, starlikeness and convexity in the open unit disc 𝔻. Results for the Alexander transform of these generalized polylogarithm are also obtained.