Limit of a complex residue
0
$begingroup$
I was solving the residue for $frac{e^{1/x}}{x^2}$ at x = 0 found it to be 0 using Laurent series expansion.
This doubt stuck in my mind
Does this limit $lim_{p to 0}Res frac{e^{1/x}}{x^2(x-p)}$ at x = p exist?
complex-analysis limits residue-calculus
asked Dec 16 '18 at 14:16
MuraliMurali
54
$endgroup$
add a comment |
0
$begingroup$
I was solving the residue for $frac{e^{1/x}}{x^2}$ at x = 0 found it to be 0 using Laurent series expansion.
This doubt stuck in my mind
Does this limit $lim_{p to 0}Res frac{e^{1/x}}{x^2(x-p)}$ at x = p exist?
complex-analysis limits residue-calculus
asked Dec 16 '18 at 14:16
MuraliMurali
54
$endgroup$
$begingroup$
In what way is your second problem a natural extension of your first problem?
$endgroup$
– Kenny Wong
Dec 16 '18 at 14:20
$begingroup$
@KennyWong This just stuck in my mind when solving the former one. Don't know its an expansion or not.
$endgroup$
– Murali
Dec 16 '18 at 14:25
add a comment |
0
0
0
$begingroup$
I was solving the residue for $frac{e^{1/x}}{x^2}$ at x = 0 found it to be 0 using Laurent series expansion.
This doubt stuck in my mind
Does this limit $lim_{p to 0}Res frac{e^{1/x}}{x^2(x-p)}$ at x = p exist?
complex-analysis limits residue-calculus
asked Dec 16 '18 at 14:16
MuraliMurali
54
$endgroup$
I was solving the residue for $frac{e^{1/x}}{x^2}$ at x = 0 found it to be 0 using Laurent series expansion.
This doubt stuck in my mind
Does this limit $lim_{p to 0}Res frac{e^{1/x}}{x^2(x-p)}$ at x = p exist?
complex-analysis limits residue-calculus
complex-analysis limits residue-calculus
asked Dec 16 '18 at 14:16
MuraliMurali
54
asked Dec 16 '18 at 14:16
MuraliMurali
54
edited Dec 16 '18 at 14:24
Murali
asked Dec 16 '18 at 14:16
MuraliMurali
54
asked Dec 16 '18 at 14:16
MuraliMurali
54
asked Dec 16 '18 at 14:16
MuraliMurali
54
54
$begingroup$
In what way is your second problem a natural extension of your first problem?
$endgroup$
– Kenny Wong
Dec 16 '18 at 14:20
$begingroup$
@KennyWong This just stuck in my mind when solving the former one. Don't know its an expansion or not.
$endgroup$
– Murali
Dec 16 '18 at 14:25
add a comment |
$begingroup$
In what way is your second problem a natural extension of your first problem?
$endgroup$
– Kenny Wong
Dec 16 '18 at 14:20
$begingroup$
@KennyWong This just stuck in my mind when solving the former one. Don't know its an expansion or not.
$endgroup$
– Murali
Dec 16 '18 at 14:25
$begingroup$
In what way is your second problem a natural extension of your first problem?
$endgroup$
– Kenny Wong
Dec 16 '18 at 14:20
$begingroup$
In what way is your second problem a natural extension of your first problem?
$endgroup$
– Kenny Wong
Dec 16 '18 at 14:20
$begingroup$
@KennyWong This just stuck in my mind when solving the former one. Don't know its an expansion or not.
$endgroup$
– Murali
Dec 16 '18 at 14:25
$begingroup$
@KennyWong This just stuck in my mind when solving the former one. Don't know its an expansion or not.
$endgroup$
– Murali
Dec 16 '18 at 14:25
add a comment |
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
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3042656%2flimit-of-a-complex-residue%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
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3042656%2flimit-of-a-complex-residue%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
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
$begingroup$
In what way is your second problem a natural extension of your first problem?
$endgroup$
– Kenny Wong
Dec 16 '18 at 14:20
$begingroup$
@KennyWong This just stuck in my mind when solving the former one. Don't know its an expansion or not.
$endgroup$
– Murali
Dec 16 '18 at 14:25