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Definitions: Holomorphic and complex differentiable functions HELP PLEASE Watch

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    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
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    From what is know, a complex function w=f(z) is analytic at a point z_{0} if f

    is differentiable at z_{0} and at every point in some neighbourhood of z_{0} (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)
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    (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.
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    (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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