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# Definitions: Holomorphic and complex differentiable functions HELP PLEASE watch

1. Definition: A complex function is holomorphic (or analytic) at z0 if it is complex differentiable on some disc centre z0

Can someone please tell me what a disc centre is?? Is it just a point or is it the centre of the disc which would be the origin..?

If a function is complex differentiable at a point on the complex plane does that mean it is holomorphic on the entire plane or just at that point
2. From what is know, a complex function is analytic at a point if

is differentiable at and at every point in some neighbourhood of (the disk thingy).

A function is analytic in a domain D if it is analytic at every point in the domain D - (holomorphic)

(as opposed to analytic in entire complex plane = entire)
3. (Original post by CammieInfinity)
Definition: A complex function is holomorphic (or analytic) at z0 if it is complex differentiable on some disc centre z0

Can someone please tell me what a disc centre is?? Is it just a point or is it the centre of the disc which would be the origin..?

If a function is complex differentiable at a point on the complex plane does that mean it is holomorphic on the entire plane or just at that point
A disc is basically a "filled in circle" i.e. a circle and its interior, so a disc centre z0 would be a set of points z satisfying |z - z0| <= r for some positive number r.
4. (Original post by CammieInfinity)
Definition: A complex function is holomorphic (or analytic) at z0 if it is complex differentiable on some disc centre z0

Can someone please tell me what a disc centre is?? Is it just a point or is it the centre of the disc which would be the origin..?

If a function is complex differentiable at a point on the complex plane does that mean it is holomorphic on the entire plane or just at that point
"Disc centre" should be read as "disc with centre".

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