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










0






active

oldest

votes












Your Answer





StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");

StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});

function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});


}
});














draft saved

draft discarded


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3074673%2fshow-a-function-cannot-be-the-derivative-of-an-entire-function-complex-analysis%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown

























0






active

oldest

votes








0






active

oldest

votes









active

oldest

votes






active

oldest

votes
















draft saved

draft discarded




















































Thanks for contributing an answer to Mathematics Stack Exchange!


  • Please be sure to answer the question. Provide details and share your research!

But avoid



  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.


Use MathJax to format equations. MathJax reference.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3074673%2fshow-a-function-cannot-be-the-derivative-of-an-entire-function-complex-analysis%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







Popular posts from this blog

Human spaceflight

Can not write log (Is /dev/pts mounted?) - openpty in Ubuntu-on-Windows?

File:DeusFollowingSea.jpg