Show a function cannot be the derivative of an entire function (complex analysis)












0












$begingroup$


Suppose we are given two complex integrals along contours both $4overline{z}$ with paths.



I would like to know how to prove the function $f(z)=4overline{z}$ cannot be the derivative of an entire function.



How would I go about proving this using the two integrals of $4overline{z}$ I calculated originally?



Thank you very much.










share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    I suppose that (z bar) is $bar z$, the complex conjugate of $z$. Do you know that this is not an analytic function?
    $endgroup$
    – Emilio Novati
    Jan 15 at 17:30
















0












$begingroup$


Suppose we are given two complex integrals along contours both $4overline{z}$ with paths.



I would like to know how to prove the function $f(z)=4overline{z}$ cannot be the derivative of an entire function.



How would I go about proving this using the two integrals of $4overline{z}$ I calculated originally?



Thank you very much.










share|cite|improve this question











$endgroup$








  • 1




    $begingroup$
    I suppose that (z bar) is $bar z$, the complex conjugate of $z$. Do you know that this is not an analytic function?
    $endgroup$
    – Emilio Novati
    Jan 15 at 17:30














0












0








0





$begingroup$


Suppose we are given two complex integrals along contours both $4overline{z}$ with paths.



I would like to know how to prove the function $f(z)=4overline{z}$ cannot be the derivative of an entire function.



How would I go about proving this using the two integrals of $4overline{z}$ I calculated originally?



Thank you very much.










share|cite|improve this question











$endgroup$




Suppose we are given two complex integrals along contours both $4overline{z}$ with paths.



I would like to know how to prove the function $f(z)=4overline{z}$ cannot be the derivative of an entire function.



How would I go about proving this using the two integrals of $4overline{z}$ I calculated originally?



Thank you very much.







complex-analysis






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 19 at 11:29









JustDroppedIn

2,238420




2,238420










asked Jan 15 at 17:26









REKXREKX

32




32








  • 1




    $begingroup$
    I suppose that (z bar) is $bar z$, the complex conjugate of $z$. Do you know that this is not an analytic function?
    $endgroup$
    – Emilio Novati
    Jan 15 at 17:30














  • 1




    $begingroup$
    I suppose that (z bar) is $bar z$, the complex conjugate of $z$. Do you know that this is not an analytic function?
    $endgroup$
    – Emilio Novati
    Jan 15 at 17:30








1




1




$begingroup$
I suppose that (z bar) is $bar z$, the complex conjugate of $z$. Do you know that this is not an analytic function?
$endgroup$
– Emilio Novati
Jan 15 at 17:30




$begingroup$
I suppose that (z bar) is $bar z$, the complex conjugate of $z$. Do you know that this is not an analytic function?
$endgroup$
– Emilio Novati
Jan 15 at 17:30










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