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    question on uniqueness theorem:

    let f be an entire function s.t

    f(i/n)=cos(1/n) for n a positive integer

    show f(z)=cosh (z)

    done this by considering S={i/n for n positive integer} noting both f and cosh agree on S and S has limit point.

    the next part is

    ii) find an entire function f other than f(z)=cosh(z)) that satisfies

    f(in)=cos n for n a positive integer

    can I just put something like

    f(z)=sin(2(pi)z/i) + cos (z/i)? is there any deep justification for any function apart from cosh(z)?

    can someone explain how the uniqueness theorem fails on part(ii)

    thanks
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    (Original post by mathz)
    question on uniqueness theorem:

    let f be an entire function s.t

    f(i/n)=cos(1/n) for n a positive integer

    show f(z)=cosh (z)

    done this by considering S={i/n for n positive integer} noting both f and cosh agree on S and S has limit point.

    the next part is

    ii) find an entire function f other than f(z)=cosh(z)) that satisfies

    f(in)=cos n for n a positive integer

    can I just put something like

    f(z)=sin(2(pi)z/i) + cos (z/i)? is there any deep justification for any function apart from cosh(z)?

    can someone explain how the uniqueness theorem fails on part(ii)

    thanks
    Your answer seems fine for the second part

    The uniqueness theorem doesn't apply as the points don't have a limit point in this case.
 
 
 
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