This question is part of a bigger one, but I need to determine for what domain is entire. I am not sure how to get started. I suspect I am having a really stupid moment and just can't figure out how to make it fit into Cauchy-Riemann, but I can't work it out. Thanks for your help.
Entire Function -- from Wolfram MathWorld
... according to the 'standard definition', an f(z) is called entire if it is analytic on the whole complex plane . That means that in any case the expression 'for what domain is entire' is 'selfcontraductory' and the expression 'for what domain is analytic' should be used instead of it...