If a complex function 
is analytic in a disk
contained in a simply connected domain 
and 
can be analytically continued
along every polygonal arc in 
, then 
can be analytically continued
to a single-valued analytic function on all
of 
!
Monodromy Theorem
See also
Analytic ContinuationExplore with Wolfram|Alpha
References
Flanigan, F. J. Complex Variables: Harmonic and Analytic Functions. New York: Dover, p. 234, 1983.Knopp, K. "The Monodromy Theorem." §25 in Theory of Functions Parts I and II, Two Volumes Bound as One, Part I. New York: Dover, pp. 105-111, 1996.Krantz, S. G. "The Monodromy Theorem." §10.3.5 in Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 134, 1999.Referenced on Wolfram|Alpha
Monodromy TheoremCite this as:
Weisstein, Eric W. "Monodromy Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MonodromyTheorem.html