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In this paper, we compute the reproducing kernel Bm,αz,w for the generalized Fock space Fm,α2ℂ. The usual Fock space is the case when m=2. We express the reproducing kernel in terms of a suitable hypergeometric series  1Fq. In particular, we show that there is a close connection between B4,αz,w and the error function. We also obtain the closed forms of Bm,αz,w when m=1,2/3,1/2. Finally, we also prove that Bm,αz,z~eαzmzm−2 as ∣z∣⟶∞.