Investigation of the Hypotheses of Khuti's Theorem on Regge-Polf Asymptotes

The hypotheses of Khuri's theorem, which imply that asymptotes of Regge trajectories cannot be infinite, are studied. We show that the residue function $\beta \mathrm{}\left(s\right)\mathrm{}$ is expected to have an essential singularity at infinity and that $\alpha \mathrm{}\left(s\right)\mathrm{}$ may well have complex branchpoints, making Khuri's theorem consistent with infinite asymptotes.