Jensen's Formula

A relation connecting the values of a meromorphic function inside a disk with its boundary values on the circumference and with its zeros and poles (Jensen 1899, Levin 1980). Let  be holomorphic on a neighborhood of the closed disk  and , , ...,  be the zeros of  in the open disk  counted according to their multiplicities, and assume that  on . Then

(Krantz 1999, p. 118).

REFERENCES:

Borwein, P. and Erdélyi, T. "Jensen's Formula." §4.2.E.10c in Polynomials and Polynomial Inequalities. New York: Springer-Verlag, p. 187, 1995.

Jensen, J. L. "Sur un nouvel et important théorème de la théorie des fonctions." Acta Math. 22, 359-364, 1899.

Krantz, S. G. "Jensen's Formula." §9.1.2 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 117-118, 1999.

Levin, B. Ya. Distribution of Zeros of Entire Functions. Providence, RI: Amer. Math. Soc., 1980.