Lindelöf's theorem gives an upper bound for a function 
that is continuous on the
closed half-strip ![D={s:sigma_1<=Re[s]<=sigma_2, Im[s]>=t_0}](/images/equations/LindeloefsTheorem/Inline2.svg)
and analytic in its interior,
where 
and 
are real constants. If
on the boundary 
and there is a real constant 
such that 
is bounded
on 
, then 
throughout 
(Edwards 2001).
Lindelöf's Theorem
See also
Lindelöf Hypothesis, Lindelöf's Catenary TheoremExplore with Wolfram|Alpha
References
Edwards, H. M. Riemann's Zeta Function. New York: Dover, p. 184, 2001.Lindelöf, E. "Quelques 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