+- Tetration Forum (https://math.eretrandre.org/tetrationforum)
+-- Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1)
+--- Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3)
+--- Thread: Look-alike functions. (/showthread.php?tid=1070)
Look-alike functions. - tommy1729 - 03/07/2016
Consider the argument of An entire function within a unit radius.
If they are identical for 2 distinct entire function with that radius we call them " look-alike ".
For instance 2sinh(z+3) and exp(z+3) are look-alikes.
You might have noticed that all look-alikes to the above satisfy
F ' ' (z) = F(z).
So yes this relates to differential equations.
I think cauchy-riemann matters.
This is probably isomorphic to something well understood.
Regards
Tommy1729
RE: Look-alike functions. - hixidom - 03/08/2016
sinh(t) is defined in terms of exp(t). Why is it notable that they are similar sometimes?