Let 
be an analytic function in an angular domain
.
Suppose there is a constant 
such that for each 
, each finite boundary point has a neighborhood
such that 
on the intersection of 
with this neighborhood, and
that for some positive number 
for sufficiently large 
, the inequality 
holds. Then 
in 
.
Phragmén-Lindêlöf Theorem
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References
Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 160, 1980.Referenced on Wolfram|Alpha
Phragmén-Lindêlöf TheoremCite this as:
Weisstein, Eric W. "Phragmén-Lindêlöf Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Phragmen-LindeloefTheorem.html