# 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