Solve the functional equation:

, where .

P.S. Good luck!

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- Jun 29th 2010, 05:14 AMDeMathFunctional equation
Solve the functional equation:

, where .

P.S. Good luck! - Jun 29th 2010, 06:48 AMNonCommAlg
it seems that are all the solutions ...

- Jun 29th 2010, 06:52 AMshostakovich
let b=beta

taking the logarithm of the both sides , we get :

, let

we get :

dividing both sides by :

let :

we have : which is equivalent to : , if i remember well , the solution of the Last equation is for some real a , a difficult result of Erdos !! - Jun 29th 2010, 06:56 AMNonCommAlg
you'd need some sort of continuity condition i guess. anyway, just put to end up with the simple equation

- Jun 29th 2010, 07:01 AMDeMath
- Jun 29th 2010, 07:08 AMNonCommAlg