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Scale-periodic harmonic function from an elliptic function
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Partial differential equation
Harmonic function
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Words: 48
Let
℘
Λ
be the
Weierstrass elliptic function
for
Λ
=
(
lo
g
q
)
Z
+
2
πi
Z
,
q
>
1.
(420)
Because
2
πi
is a
period
, the formula
u
(
z
)
=
Re
℘
Λ
(
lo
g
z
)
(421)
is independent of the branch of the
complex logarithm
. It is a nonconstant harmonic function on
C
∗
∖
{
q
m
:
m
∈
Z
}
(422)
and its other period gives
u
(
q
z
)
=
u
(
z
)
.
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(6)
Harmonic function
Partial differential equation
Analysis
Area of mathematics
Mathematics
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