A sum of products ? - Printable Version +- Tetration Forum ( https://tetrationforum.org)+-- Forum: Tetration and Related Topics ( https://tetrationforum.org/forumdisplay.php?fid=1)+--- Forum: Mathematical and General Discussion ( https://tetrationforum.org/forumdisplay.php?fid=3)+--- Thread: A sum of products ? ( /showthread.php?tid=803) |

A sum of products ? - tommy1729 - 08/11/2013
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 |