Asymptotic Behavior of Stieltjes Transforms. I
W.S. Woolcock · Journal of Mathematical Physics · 1967
Several theorems are proved concerning the asymptotic behavior of Stieltjes transforms as |z| approaches infinity, in a sector of the complex z plane which does not include the cut in the transform. The asymptotic behavior of the transform is related to the asymptotic behavior, for large values of the argument, of the function whose transform is taken.