You are using a browser not supported by the Wolfram Cloud
Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.
I understand and wish to continue anyway »
WOLFRAM NOTEBOOK
Properties of Rosette Functions
Properties of Rosette Functions
This Demonstration illustrates the following theorems:
If, in the sum , we have =0 unless , is a rosette function with -fold symmetry.
f(z)=∑
a
nm
n
z
m
z
a
nm
n≡m(modp)
f
p
If, in the sum , we have =0 unless , is a rosette function with -fold symmetry.
f(z)=
∞
∑
-∞
a
n
n
z
a
n
n≡0(modp)
f
p
If, in the sum , we have =, is a function with mirror symmetry.
f(z)=
∞
∑
-∞
a
nm
n
z
m
z
a
nm
a
mn
f
The functions and are defined as and .
f
g
f(z)=c+a+b
n
z
-n
z
g(z)=c+a(+)+b(+)
n
z
n
z
3n
z
n
z
n
z
3n
z