Collect Fourier series terms
$begingroup$
Is there a way to make mathematica automatically collect terms like $mathrm{Cos}[n x]$ with $n=1,2,3...$?
I have a long expression coming out of a Fourier series where I see a lot of $Cos[x],Cos[2 x],Cos[3 x]$ and so on, but Simplify is very inefficient. I would like mathematica to automatically collect all coefficients of the various Cos[n x] without having to do it manually for each one of them.
coefficients
asked Apr 6 at 16:49
RiccardoRiccardo
505
$endgroup$
add a comment |
$begingroup$
Is there a way to make mathematica automatically collect terms like $mathrm{Cos}[n x]$ with $n=1,2,3...$?
I have a long expression coming out of a Fourier series where I see a lot of $Cos[x],Cos[2 x],Cos[3 x]$ and so on, but Simplify is very inefficient. I would like mathematica to automatically collect all coefficients of the various Cos[n x] without having to do it manually for each one of them.
coefficients
asked Apr 6 at 16:49
RiccardoRiccardo
505
$endgroup$
$begingroup$
can you show your initial code, so we try to help!
$endgroup$
– Alrubaie
Apr 6 at 17:00
$begingroup$
TryCollect[exp /. Cos[x n_.] -> x^n, x]/. x^n_. -> Cos[n x].
$endgroup$
– Somos
2 days ago
add a comment |
$begingroup$
Is there a way to make mathematica automatically collect terms like $mathrm{Cos}[n x]$ with $n=1,2,3...$?
I have a long expression coming out of a Fourier series where I see a lot of $Cos[x],Cos[2 x],Cos[3 x]$ and so on, but Simplify is very inefficient. I would like mathematica to automatically collect all coefficients of the various Cos[n x] without having to do it manually for each one of them.
coefficients
asked Apr 6 at 16:49
RiccardoRiccardo
505
$endgroup$
Is there a way to make mathematica automatically collect terms like $mathrm{Cos}[n x]$ with $n=1,2,3...$?
I have a long expression coming out of a Fourier series where I see a lot of $Cos[x],Cos[2 x],Cos[3 x]$ and so on, but Simplify is very inefficient. I would like mathematica to automatically collect all coefficients of the various Cos[n x] without having to do it manually for each one of them.
coefficients
coefficients
asked Apr 6 at 16:49
RiccardoRiccardo
505
asked Apr 6 at 16:49
RiccardoRiccardo
505
asked Apr 6 at 16:49
RiccardoRiccardo
505
asked Apr 6 at 16:49
RiccardoRiccardo
505
asked Apr 6 at 16:49
RiccardoRiccardo
505
505
$begingroup$
can you show your initial code, so we try to help!
$endgroup$
– Alrubaie
Apr 6 at 17:00
$begingroup$
TryCollect[exp /. Cos[x n_.] -> x^n, x]/. x^n_. -> Cos[n x].
$endgroup$
– Somos
2 days ago
add a comment |
$begingroup$
can you show your initial code, so we try to help!
$endgroup$
– Alrubaie
Apr 6 at 17:00
$begingroup$
TryCollect[exp /. Cos[x n_.] -> x^n, x]/. x^n_. -> Cos[n x].
$endgroup$
– Somos
2 days ago
$begingroup$
can you show your initial code, so we try to help!
$endgroup$
– Alrubaie
Apr 6 at 17:00
$begingroup$
can you show your initial code, so we try to help!
$endgroup$
– Alrubaie
Apr 6 at 17:00
$begingroup$
Try
Collect[exp /. Cos[x n_.] -> x^n, x]/. x^n_. -> Cos[n x].$endgroup$
– Somos
2 days ago
$begingroup$
Try
Collect[exp /. Cos[x n_.] -> x^n, x]/. x^n_. -> Cos[n x].$endgroup$
– Somos
2 days ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
is this what you are asking?
exp=3Cos[x]+5Cos[2x]+12Cos[3x];
Coefficient[exp,Cos[x #]]&/@Range@3
{3, 5, 12}
answered Apr 6 at 17:24
J42161217J42161217
4,273324
$endgroup$
$begingroup$
Yes, thanks this is it!
$endgroup$
– Riccardo
Apr 6 at 17:28
$begingroup$
you are welcome!
$endgroup$
– J42161217
Apr 6 at 17:35
add a comment |
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: "387"
};
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: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
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
},
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
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%2fmathematica.stackexchange.com%2fquestions%2f194735%2fcollect-fourier-series-terms%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
is this what you are asking?
exp=3Cos[x]+5Cos[2x]+12Cos[3x];
Coefficient[exp,Cos[x #]]&/@Range@3
{3, 5, 12}
answered Apr 6 at 17:24
J42161217J42161217
4,273324
$endgroup$
$begingroup$
Yes, thanks this is it!
$endgroup$
– Riccardo
Apr 6 at 17:28
$begingroup$
you are welcome!
$endgroup$
– J42161217
Apr 6 at 17:35
add a comment |
$begingroup$
is this what you are asking?
exp=3Cos[x]+5Cos[2x]+12Cos[3x];
Coefficient[exp,Cos[x #]]&/@Range@3
{3, 5, 12}
answered Apr 6 at 17:24
J42161217J42161217
4,273324
$endgroup$
$begingroup$
Yes, thanks this is it!
$endgroup$
– Riccardo
Apr 6 at 17:28
$begingroup$
you are welcome!
$endgroup$
– J42161217
Apr 6 at 17:35
add a comment |
$begingroup$
is this what you are asking?
exp=3Cos[x]+5Cos[2x]+12Cos[3x];
Coefficient[exp,Cos[x #]]&/@Range@3
{3, 5, 12}
answered Apr 6 at 17:24
J42161217J42161217
4,273324
$endgroup$
is this what you are asking?
exp=3Cos[x]+5Cos[2x]+12Cos[3x];
Coefficient[exp,Cos[x #]]&/@Range@3
{3, 5, 12}
answered Apr 6 at 17:24
J42161217J42161217
4,273324
edited Apr 6 at 17:34
answered Apr 6 at 17:24
J42161217J42161217
4,273324
answered Apr 6 at 17:24
J42161217J42161217
4,273324
answered Apr 6 at 17:24
J42161217J42161217
4,273324
4,273324
$begingroup$
Yes, thanks this is it!
$endgroup$
– Riccardo
Apr 6 at 17:28
$begingroup$
you are welcome!
$endgroup$
– J42161217
Apr 6 at 17:35
add a comment |
$begingroup$
Yes, thanks this is it!
$endgroup$
– Riccardo
Apr 6 at 17:28
$begingroup$
you are welcome!
$endgroup$
– J42161217
Apr 6 at 17:35
$begingroup$
Yes, thanks this is it!
$endgroup$
– Riccardo
Apr 6 at 17:28
$begingroup$
Yes, thanks this is it!
$endgroup$
– Riccardo
Apr 6 at 17:28
$begingroup$
you are welcome!
$endgroup$
– J42161217
Apr 6 at 17:35
$begingroup$
you are welcome!
$endgroup$
– J42161217
Apr 6 at 17:35
add a comment |
Thanks for contributing an answer to Mathematica 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.
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%2fmathematica.stackexchange.com%2fquestions%2f194735%2fcollect-fourier-series-terms%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
$begingroup$
can you show your initial code, so we try to help!
$endgroup$
– Alrubaie
Apr 6 at 17:00
$begingroup$
Try
Collect[exp /. Cos[x n_.] -> x^n, x]/. x^n_. -> Cos[n x].$endgroup$
– Somos
2 days ago