Jensen's formula (after Johan Jensen) in complex analysis relates the behaviour of an analytic function on a circle with the moduli of the zeros inside the circle, and is important in the study of entire functions.

The statement of Jensen's formula is

If $f$ is an analytic function in a region which contains the closed disk D in the complex plane, if $a\_1,\; a\_2,dots,a\_n$ are the zeros of $f$ in the interior of D repeated according to multiplicity, and if $f(0)ne\; 0$, then

$log\; |f(0)|\; =\; -sum\_\{k=1\}^n\; logleft(frac\{r\}$>right)+frac{1}{2pi}int_0^{2pi}log|f(re^{itheta})|dtheta.

This formula establishes a connection between the moduli of the zeros of the function f inside the disk

References

• L. V. Ahlfors (1979). Complex Analysis. McGraw-Hill. ISBN 0-07-000657-1.