08/11/2013, 08:19 PM

Inspired by the famous Weierstrass I wondered about the following.

Let f(z) be an entire function.

how to find f(z) = A(z) + B(z) =

(z^a exp(a(z)) product_n [(1-z/a_n)^(a*_n)]) +

(z^a exp(b(z)) product_n [1-z/b_n]^(b*_n)])

with a,a*_n the multiplicities of the zero's of A : 0,a_n.

with a,b*_n the multiplicities of the zero's of B : 0,b_n.

with a(z) and b(z) entire functions.

Of course nontrivial ways , not such as f(z) = A(z) + A(z) for some f(z).

regards

tommy1729

Let f(z) be an entire function.

how to find f(z) = A(z) + B(z) =

(z^a exp(a(z)) product_n [(1-z/a_n)^(a*_n)]) +

(z^a exp(b(z)) product_n [1-z/b_n]^(b*_n)])

with a,a*_n the multiplicities of the zero's of A : 0,a_n.

with a,b*_n the multiplicities of the zero's of B : 0,b_n.

with a(z) and b(z) entire functions.

Of course nontrivial ways , not such as f(z) = A(z) + A(z) for some f(z).

regards

tommy1729