WOLFRAM|DEMONSTRATIONS PROJECT

Properties of Rosette Functions

​
cyclic
dihedral
a
b
p-fold
4
This Demonstration illustrates the following theorems:
If, in the sum
f(z)=∑
a
nm
n
z
m
z
, we have
a
nm
=0
unless
n≡m(modp)
,
f
is a rosette function with
p
-fold symmetry.
If, in the sum
f(z)=
∞
∑
-∞
a
n
n
z
, we have
a
n
=0
unless
n≡0(modp)
,
f
is a rosette function with
p
-fold symmetry.
If, in the sum
f(z)=
∞
∑
-∞
a
nm
n
z
m
z
, we have
a
nm
=
a
mn
,
f
is a function with mirror symmetry.
The functions
f
and
g
are defined as
f(z)=c+a
n
z
+b
-n
z
and
g(z)=c+a(
n
z
+
n
z
)+b(
3n
z
n
z
+
n
z
3n
z
)
.