  We invoke integrals of Mellin-Barnes type to analytically continue the
Gopakumar-Vafa resummation of the topological string free energy in the string
coupling constant, leading to additional non-perturbative terms. We also
discuss in a similar manner the refined and Nekrasov-Shatashvili limit version
thereof. The derivation is straight-forward and essentially boils down to
taking residue. This allows us to confirm some related conjectures in the
literature at tree-level.
