Show a function cannot be the derivative of an entire function (complex analysis)
$begingroup$
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.
complex-analysis
edited Jan 19 at 11:29
JustDroppedIn
2,375420
asked Jan 15 at 17:26
REKXREKX
32
$endgroup$
add a comment |
$begingroup$
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.
complex-analysis
edited Jan 19 at 11:29
JustDroppedIn
2,375420
asked Jan 15 at 17:26
REKXREKX
32
$endgroup$
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
add a comment |
$begingroup$
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.
complex-analysis
edited Jan 19 at 11:29
JustDroppedIn
2,375420
asked Jan 15 at 17:26
REKXREKX
32
$endgroup$
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
complex-analysis
edited Jan 19 at 11:29
JustDroppedIn
2,375420
asked Jan 15 at 17:26
REKXREKX
32
edited Jan 19 at 11:29
JustDroppedIn
2,375420
asked Jan 15 at 17:26
REKXREKX
32
edited Jan 19 at 11:29
JustDroppedIn
2,375420
edited Jan 19 at 11:29
JustDroppedIn
2,375420
edited Jan 19 at 11:29
JustDroppedIn
2,375420
2,375420
asked Jan 15 at 17:26
REKXREKX
32
asked Jan 15 at 17:26
REKXREKX
32
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
add a comment |
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
add a comment |
0
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$begingroup$
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