MathDB

F(s)/Gamma(s) bounded on Re(s)>0

Source: Miklós Schweitzer 2016, Problem 6

November 2, 2016

complex analysisGamma function

Problem Statement

Let

\Gamma(s)

denote Euler's gamma function. Construct an even entire function

F(s)

that does not vanish everywhere, for which the quotient

F(s)/\Gamma(s)

is bounded on the right halfplane

\{\Re(s)>0\}