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Miklós Schweitzer
2016 Miklós Schweitzer
6
6
Part of
2016 Miklós Schweitzer
Problems
(1)
F(s)/Gamma(s) bounded on Re(s)>0
Source: Miklós Schweitzer 2016, Problem 6
11/2/2016
Let
Γ
(
s
)
\Gamma(s)
Γ
(
s
)
denote Euler's gamma function. Construct an even entire function
F
(
s
)
F(s)
F
(
s
)
that does not vanish everywhere, for which the quotient
F
(
s
)
/
Γ
(
s
)
F(s)/\Gamma(s)
F
(
s
)
/Γ
(
s
)
is bounded on the right halfplane
{
ℜ
(
s
)
>
0
}
\{\Re(s)>0\}
{
ℜ
(
s
)
>
0
}
.
complex analysis
Gamma function