Proof that the following function is continuous and (hence holomorphic using Morera's).

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
0
down vote

favorite












enter image description here



How does one go about proving that g is continuous?
I can't seem to find a bound for the integral. Secondly what happens when z is a element of the curve. I know that the function inside the integral is still continuous but I won't be able to split it up to manipulate it.



Any Solutions?(Stuck for 6 hours) I have proven for z in H. Just need a proof for in G










share|cite|improve this question























  • Related question.
    – Jan Bohr
    Sep 5 at 11:55











  • the map "$int _x$" that sends $fmapsto int f dx$ is continuous. so you have composition of continuous functions. $int_w circ phi(_,w) $
    – Sheve
    Sep 5 at 11:56














up vote
0
down vote

favorite












enter image description here



How does one go about proving that g is continuous?
I can't seem to find a bound for the integral. Secondly what happens when z is a element of the curve. I know that the function inside the integral is still continuous but I won't be able to split it up to manipulate it.



Any Solutions?(Stuck for 6 hours) I have proven for z in H. Just need a proof for in G










share|cite|improve this question























  • Related question.
    – Jan Bohr
    Sep 5 at 11:55











  • the map "$int _x$" that sends $fmapsto int f dx$ is continuous. so you have composition of continuous functions. $int_w circ phi(_,w) $
    – Sheve
    Sep 5 at 11:56












up vote
0
down vote

favorite









up vote
0
down vote

favorite











enter image description here



How does one go about proving that g is continuous?
I can't seem to find a bound for the integral. Secondly what happens when z is a element of the curve. I know that the function inside the integral is still continuous but I won't be able to split it up to manipulate it.



Any Solutions?(Stuck for 6 hours) I have proven for z in H. Just need a proof for in G










share|cite|improve this question















enter image description here



How does one go about proving that g is continuous?
I can't seem to find a bound for the integral. Secondly what happens when z is a element of the curve. I know that the function inside the integral is still continuous but I won't be able to split it up to manipulate it.



Any Solutions?(Stuck for 6 hours) I have proven for z in H. Just need a proof for in G







complex-analysis continuity holomorphic-functions






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Sep 5 at 12:06

























asked Sep 5 at 11:44









Jhon Doe

423212




423212











  • Related question.
    – Jan Bohr
    Sep 5 at 11:55











  • the map "$int _x$" that sends $fmapsto int f dx$ is continuous. so you have composition of continuous functions. $int_w circ phi(_,w) $
    – Sheve
    Sep 5 at 11:56
















  • Related question.
    – Jan Bohr
    Sep 5 at 11:55











  • the map "$int _x$" that sends $fmapsto int f dx$ is continuous. so you have composition of continuous functions. $int_w circ phi(_,w) $
    – Sheve
    Sep 5 at 11:56















Related question.
– Jan Bohr
Sep 5 at 11:55





Related question.
– Jan Bohr
Sep 5 at 11:55













the map "$int _x$" that sends $fmapsto int f dx$ is continuous. so you have composition of continuous functions. $int_w circ phi(_,w) $
– Sheve
Sep 5 at 11:56




the map "$int _x$" that sends $fmapsto int f dx$ is continuous. so you have composition of continuous functions. $int_w circ phi(_,w) $
– Sheve
Sep 5 at 11:56















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',
convertImagesToLinks: true,
noModals: false,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
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%2f2906162%2fproof-that-the-following-function-is-continuous-and-hence-holomorphic-using-mor%23new-answer', 'question_page');

);

Post as a guest



































active

oldest

votes













active

oldest

votes









active

oldest

votes






active

oldest

votes















 

draft saved


draft discarded















































 


draft saved


draft discarded














StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2906162%2fproof-that-the-following-function-is-continuous-and-hence-holomorphic-using-mor%23new-answer', 'question_page');

);

Post as a guest













































































這個網誌中的熱門文章

How to combine Bézier curves to a surface?

Mutual Information Always Non-negative

Why am i infinitely getting the same tweet with the Twitter Search API?