Definitions

# Jensen's formula

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 $f\left(0\right)ne 0$, then
$log |f\left(0\right)| = -sum_\left\{k=1\right\}^n logleft\left(frac\left\{r\right\}$
>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.

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