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 f be holomorphic on a neighborhood of the closed disk D^_(0,r) and f(0)!=0, a_1, ..., a_k be the zeros of f in the open disk D(0,r) counted according to their multiplicities, and assume that f!=0 on partialD(0,r). Then


(Krantz 1999, p. 118).

See also

Contour Integral, Jensen's Inequality, Mahler Measure

Portions of this entry contributed by Ronald M. Aarts

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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.

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Jensen's Formula

Cite this as:

Aarts, Ronald M. and Weisstein, Eric W. "Jensen's Formula." From MathWorld--A Wolfram Web Resource.

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