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 $f(0)\; e\; 0$, then ::$log\; |f(0)|\; =\; -sum\_\{k=1\}^n\; logleft(frac\{r\}\; ight)+frac\{1\}\{2pi\}int\_0^\{2pi\}log|f(re^\{i\; heta\})|d\; heta.$This formula establishes a connection between the moduli of the zeros of the function "f" inside the disk

References

*cite book | author = L. V. Ahlfors| title = Complex Analysis | publisher = McGraw-Hill | year = 1979 | id=ISBN 0-07-000657-1