Jensen,s Formula
المؤلف:
Levin, B.
المصدر:
Ya. Distribution of Zeros of Entire Functions. Providence, RI: Amer. Math. Soc., 1980.
الجزء والصفحة:
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17-11-2018
843
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.
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