If an analytic function has a single simple pole at the radius of convergence of its power series, then the ratio of the coefficients of its power series converges to that pole.
König's Theorem
See also
König-Egeváry Theorem, König's Line Coloring Theorem, PoleExplore with Wolfram|Alpha
References
König, J. "Über eine Eigenschaft der Potenzreihen." Math. Ann. 23, 447-449, 1884.Referenced on Wolfram|Alpha
König's TheoremCite this as:
Weisstein, Eric W. "König's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KoenigsTheorem.html