Recent content by intangible

Can there be a definite solution for positive real values of a? My musings so far: 0^{ix} = e^{ix\ln0} = (\cos x + i\sin x)^{\ln0} = ( \cos x + i\sin x )^{-\infty} = \left( e^{-\infty} \right)^\ln( \cos x + i\sin x ) } = 0^{\ln( \cos x + i\sin x )} Since 0^0 can be assigned to produce...

Thanks to everyone participating, I think I got sorted it out by inspecting a similar behaving sine and its infinite product. \sin x = x \prod_{n = 1}^\infty\left(1 - \frac{x^2}{\pi^2 n^2}\right) If we assume Asin(pi*A*x)=Bsin(pi*B*x) we may easily inspect the existence of trivial roots...

Acos(A*x)-Bcos(B*x)=0, where A>B Is there a general solution for an equation of this form? Thanks, intangible