Lindelöf's theorem gives a bound for a function 
that is defined and analytic
in a half-strip ![D={s:sigma_1<=Re[s]<=sigma_2,Im[s]>=t_0 0}](/images/equations/LindeloefsTheorem/Inline2.svg)
.
If 
on the boundary 
of 
and there is a constant 
such that 
is bounded on 
, then 
throughout 
(Edwards 2001).
Lindelöf's Theorem
See also
Lindelöf's Catenary Theorem, Lindelöf HypothesisExplore with Wolfram|Alpha
References
Edwards, H. M. Riemann's Zeta Function. New York: Dover, p. 184, 2001.Lindelöf, E. "Quelque remarques sur la croissance de la fonction
." Bull. Sci. Math. 32, 341-356, 1908.
Cite this as:
Weisstein, Eric W. "Lindelöf's Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LindeloefsTheorem.html