Is there an accepted notation for the nth sum/integral of a function?












2












$begingroup$


I'm working on a thesis in image processing at the moment, and wanted to include a portion concerning the methodology for n dimension images (it will include a fully write up and functioning code for 2D and 3D images), and that would involve taking the nth integral of a function of n variables, which in this case would mean the nth sum. For the sum portion, it would something like the sum of x_1 from 0 to M, then the sum of x_1 from 0 to M, and so on with a total of of N summations.



Is there any sort of widely accepted convention for annotating this, or should I just put something like sum1 of sum2 /dots then the last sum?



edit: specific examples (sorry, didn't know you could use LaTeX here):



2D: $$sum_{x_1=0}^M sum_{x_2=0}^M f(x_1,x_2)$$
3D: $$sum_{x_1=0}^M sum_{x_2=0}^M sum_{x_3=0}^M f(x_1,x_2,x_3)$$
Is there a nicer way to express something like:
$$sum_{x_1=0}^M sum_{x_2=0}^M dots sum_{x_n=0}^M f(x_1,x_2,dots,x_n)$$






integration functional-analysis summation







share|cite|improve this question











$endgroup$












  • $begingroup$
    Your question is not clear. Please edit it to show us an explicit calculation for $2$ and $3$ dimensional images with $M$ small (say $3$).
    $endgroup$
    – Ethan Bolker
    2 hours ago










  • $begingroup$
    you can also make your own notation, similar to what they do when they have the same function being applied many times e.g. $f^n(x)$ as long as you have mentioned that the function is reaplied
    $endgroup$
    – Arjang
    2 hours ago
















2












$begingroup$


I'm working on a thesis in image processing at the moment, and wanted to include a portion concerning the methodology for n dimension images (it will include a fully write up and functioning code for 2D and 3D images), and that would involve taking the nth integral of a function of n variables, which in this case would mean the nth sum. For the sum portion, it would something like the sum of x_1 from 0 to M, then the sum of x_1 from 0 to M, and so on with a total of of N summations.



Is there any sort of widely accepted convention for annotating this, or should I just put something like sum1 of sum2 /dots then the last sum?



edit: specific examples (sorry, didn't know you could use LaTeX here):



2D: $$sum_{x_1=0}^M sum_{x_2=0}^M f(x_1,x_2)$$
3D: $$sum_{x_1=0}^M sum_{x_2=0}^M sum_{x_3=0}^M f(x_1,x_2,x_3)$$
Is there a nicer way to express something like:
$$sum_{x_1=0}^M sum_{x_2=0}^M dots sum_{x_n=0}^M f(x_1,x_2,dots,x_n)$$






integration functional-analysis summation







share|cite|improve this question











$endgroup$












  • $begingroup$
    Your question is not clear. Please edit it to show us an explicit calculation for $2$ and $3$ dimensional images with $M$ small (say $3$).
    $endgroup$
    – Ethan Bolker
    2 hours ago










  • $begingroup$
    you can also make your own notation, similar to what they do when they have the same function being applied many times e.g. $f^n(x)$ as long as you have mentioned that the function is reaplied
    $endgroup$
    – Arjang
    2 hours ago














2












2








2





$begingroup$


I'm working on a thesis in image processing at the moment, and wanted to include a portion concerning the methodology for n dimension images (it will include a fully write up and functioning code for 2D and 3D images), and that would involve taking the nth integral of a function of n variables, which in this case would mean the nth sum. For the sum portion, it would something like the sum of x_1 from 0 to M, then the sum of x_1 from 0 to M, and so on with a total of of N summations.



Is there any sort of widely accepted convention for annotating this, or should I just put something like sum1 of sum2 /dots then the last sum?



edit: specific examples (sorry, didn't know you could use LaTeX here):



2D: $$sum_{x_1=0}^M sum_{x_2=0}^M f(x_1,x_2)$$
3D: $$sum_{x_1=0}^M sum_{x_2=0}^M sum_{x_3=0}^M f(x_1,x_2,x_3)$$
Is there a nicer way to express something like:
$$sum_{x_1=0}^M sum_{x_2=0}^M dots sum_{x_n=0}^M f(x_1,x_2,dots,x_n)$$






integration functional-analysis summation







share|cite|improve this question











$endgroup$




I'm working on a thesis in image processing at the moment, and wanted to include a portion concerning the methodology for n dimension images (it will include a fully write up and functioning code for 2D and 3D images), and that would involve taking the nth integral of a function of n variables, which in this case would mean the nth sum. For the sum portion, it would something like the sum of x_1 from 0 to M, then the sum of x_1 from 0 to M, and so on with a total of of N summations.



Is there any sort of widely accepted convention for annotating this, or should I just put something like sum1 of sum2 /dots then the last sum?



edit: specific examples (sorry, didn't know you could use LaTeX here):



2D: $$sum_{x_1=0}^M sum_{x_2=0}^M f(x_1,x_2)$$
3D: $$sum_{x_1=0}^M sum_{x_2=0}^M sum_{x_3=0}^M f(x_1,x_2,x_3)$$
Is there a nicer way to express something like:
$$sum_{x_1=0}^M sum_{x_2=0}^M dots sum_{x_n=0}^M f(x_1,x_2,dots,x_n)$$






integration functional-analysis summation




integration functional-analysis summation






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 2 hours ago







Peace Blaster

















asked 2 hours ago









Peace BlasterPeace Blaster

387




387












  • $begingroup$
    Your question is not clear. Please edit it to show us an explicit calculation for $2$ and $3$ dimensional images with $M$ small (say $3$).
    $endgroup$
    – Ethan Bolker
    2 hours ago










  • $begingroup$
    you can also make your own notation, similar to what they do when they have the same function being applied many times e.g. $f^n(x)$ as long as you have mentioned that the function is reaplied
    $endgroup$
    – Arjang
    2 hours ago


















  • $begingroup$
    Your question is not clear. Please edit it to show us an explicit calculation for $2$ and $3$ dimensional images with $M$ small (say $3$).
    $endgroup$
    – Ethan Bolker
    2 hours ago










  • $begingroup$
    you can also make your own notation, similar to what they do when they have the same function being applied many times e.g. $f^n(x)$ as long as you have mentioned that the function is reaplied
    $endgroup$
    – Arjang
    2 hours ago
















$begingroup$
Your question is not clear. Please edit it to show us an explicit calculation for $2$ and $3$ dimensional images with $M$ small (say $3$).
$endgroup$
– Ethan Bolker
2 hours ago




$begingroup$
Your question is not clear. Please edit it to show us an explicit calculation for $2$ and $3$ dimensional images with $M$ small (say $3$).
$endgroup$
– Ethan Bolker
2 hours ago












$begingroup$
you can also make your own notation, similar to what they do when they have the same function being applied many times e.g. $f^n(x)$ as long as you have mentioned that the function is reaplied
$endgroup$
– Arjang
2 hours ago




$begingroup$
you can also make your own notation, similar to what they do when they have the same function being applied many times e.g. $f^n(x)$ as long as you have mentioned that the function is reaplied
$endgroup$
– Arjang
2 hours ago










2 Answers
2






active

oldest

votes


















4












$begingroup$

I don't know of a convention. Your last version is perfectly clear. If you need to use it more than once then define a short symbol the first time. That could be as simple as $sum_0^M f$.



Here are two suggestions each using just a single $sum$.



$$
sum_{x in [1, 2, ldots, M]^n} f(x)
$$



$$
sum_{x_i = 0, (i = 1, ldots n)}^M f(x_i, x_2, ldots, x_n)
$$






share|cite|improve this answer









$endgroup$













  • $begingroup$
    Thanks! I just wanted to make sure I wasn't missing something glaringly obvious, though that second example looks pretty nice for when I put it in beamer and have limited space.
    $endgroup$
    – Peace Blaster
    2 hours ago



















1












$begingroup$

How about something like :
$$sum_{x_1=0}^M sum_{x_2=0}^M dots sum_{x_n=0}^M f(x_1,x_2,dots,x_n) = large]_{k=x_0}^{k=x_n}sum_{x_k=0}^{M_n}f(x_1,x_2,dots,x_n)$$



Once you use the above as definition then you can reuse it all over the place, also writing repeated sums was something that caused the the tensor notation to be invented. You might want to look up tensors instead.






share|cite|improve this answer









$endgroup$













    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%2f3104629%2fis-there-an-accepted-notation-for-the-nth-sum-integral-of-a-function%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    4












    $begingroup$

    I don't know of a convention. Your last version is perfectly clear. If you need to use it more than once then define a short symbol the first time. That could be as simple as $sum_0^M f$.



    Here are two suggestions each using just a single $sum$.



    $$
    sum_{x in [1, 2, ldots, M]^n} f(x)
    $$



    $$
    sum_{x_i = 0, (i = 1, ldots n)}^M f(x_i, x_2, ldots, x_n)
    $$






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      Thanks! I just wanted to make sure I wasn't missing something glaringly obvious, though that second example looks pretty nice for when I put it in beamer and have limited space.
      $endgroup$
      – Peace Blaster
      2 hours ago
















    4












    $begingroup$

    I don't know of a convention. Your last version is perfectly clear. If you need to use it more than once then define a short symbol the first time. That could be as simple as $sum_0^M f$.



    Here are two suggestions each using just a single $sum$.



    $$
    sum_{x in [1, 2, ldots, M]^n} f(x)
    $$



    $$
    sum_{x_i = 0, (i = 1, ldots n)}^M f(x_i, x_2, ldots, x_n)
    $$






    share|cite|improve this answer









    $endgroup$













    • $begingroup$
      Thanks! I just wanted to make sure I wasn't missing something glaringly obvious, though that second example looks pretty nice for when I put it in beamer and have limited space.
      $endgroup$
      – Peace Blaster
      2 hours ago














    4












    4








    4





    $begingroup$

    I don't know of a convention. Your last version is perfectly clear. If you need to use it more than once then define a short symbol the first time. That could be as simple as $sum_0^M f$.



    Here are two suggestions each using just a single $sum$.



    $$
    sum_{x in [1, 2, ldots, M]^n} f(x)
    $$



    $$
    sum_{x_i = 0, (i = 1, ldots n)}^M f(x_i, x_2, ldots, x_n)
    $$






    share|cite|improve this answer









    $endgroup$



    I don't know of a convention. Your last version is perfectly clear. If you need to use it more than once then define a short symbol the first time. That could be as simple as $sum_0^M f$.



    Here are two suggestions each using just a single $sum$.



    $$
    sum_{x in [1, 2, ldots, M]^n} f(x)
    $$



    $$
    sum_{x_i = 0, (i = 1, ldots n)}^M f(x_i, x_2, ldots, x_n)
    $$







    share|cite|improve this answer












    share|cite|improve this answer



    share|cite|improve this answer










    answered 2 hours ago









    Ethan BolkerEthan Bolker

    42.7k549113




    42.7k549113












    • $begingroup$
      Thanks! I just wanted to make sure I wasn't missing something glaringly obvious, though that second example looks pretty nice for when I put it in beamer and have limited space.
      $endgroup$
      – Peace Blaster
      2 hours ago


















    • $begingroup$
      Thanks! I just wanted to make sure I wasn't missing something glaringly obvious, though that second example looks pretty nice for when I put it in beamer and have limited space.
      $endgroup$
      – Peace Blaster
      2 hours ago
















    $begingroup$
    Thanks! I just wanted to make sure I wasn't missing something glaringly obvious, though that second example looks pretty nice for when I put it in beamer and have limited space.
    $endgroup$
    – Peace Blaster
    2 hours ago




    $begingroup$
    Thanks! I just wanted to make sure I wasn't missing something glaringly obvious, though that second example looks pretty nice for when I put it in beamer and have limited space.
    $endgroup$
    – Peace Blaster
    2 hours ago











    1












    $begingroup$

    How about something like :
    $$sum_{x_1=0}^M sum_{x_2=0}^M dots sum_{x_n=0}^M f(x_1,x_2,dots,x_n) = large]_{k=x_0}^{k=x_n}sum_{x_k=0}^{M_n}f(x_1,x_2,dots,x_n)$$



    Once you use the above as definition then you can reuse it all over the place, also writing repeated sums was something that caused the the tensor notation to be invented. You might want to look up tensors instead.






    share|cite|improve this answer









    $endgroup$


















      1












      $begingroup$

      How about something like :
      $$sum_{x_1=0}^M sum_{x_2=0}^M dots sum_{x_n=0}^M f(x_1,x_2,dots,x_n) = large]_{k=x_0}^{k=x_n}sum_{x_k=0}^{M_n}f(x_1,x_2,dots,x_n)$$



      Once you use the above as definition then you can reuse it all over the place, also writing repeated sums was something that caused the the tensor notation to be invented. You might want to look up tensors instead.






      share|cite|improve this answer









      $endgroup$
















        1












        1








        1





        $begingroup$

        How about something like :
        $$sum_{x_1=0}^M sum_{x_2=0}^M dots sum_{x_n=0}^M f(x_1,x_2,dots,x_n) = large]_{k=x_0}^{k=x_n}sum_{x_k=0}^{M_n}f(x_1,x_2,dots,x_n)$$



        Once you use the above as definition then you can reuse it all over the place, also writing repeated sums was something that caused the the tensor notation to be invented. You might want to look up tensors instead.






        share|cite|improve this answer









        $endgroup$



        How about something like :
        $$sum_{x_1=0}^M sum_{x_2=0}^M dots sum_{x_n=0}^M f(x_1,x_2,dots,x_n) = large]_{k=x_0}^{k=x_n}sum_{x_k=0}^{M_n}f(x_1,x_2,dots,x_n)$$



        Once you use the above as definition then you can reuse it all over the place, also writing repeated sums was something that caused the the tensor notation to be invented. You might want to look up tensors instead.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered 1 hour ago









        ArjangArjang

        5,60162363




        5,60162363






























            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%2f3104629%2fis-there-an-accepted-notation-for-the-nth-sum-integral-of-a-function%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

            Magento 2 controller redirect on button click in phtml file

            Image
            0 I want to redirect customer using controller when button is clicked in one of my phtml files. So far I got, controller: public function execute(){ return $this->addToCart(); } public function addToCart(){ // some logic $this->_redirect('checkout/cart/index'); } The above is working fine (redirecting) when you access the controller via URL (www.mydomain.com/batchorder/index/addtocart). And here is my .phtml file: $("#addToCart").click(function(){ let controllerUrl = "<?php echo $block-getUrl('batchorder/index/addtocart'); ?>" $.post(controllerUrl, { "products": JSON.stringify(sideCart.SideCartProducts) }) The post request returns my logic as it should, however, it is not redirecting. Anyone can help? ...
            Read more

            Polycentropodidae

            Image
            Polycentropodidae Plectrocnemia conspersa Siyentipiko nga pagklasipika Ginhadi-an: Animalia Phylum: Arthropoda Ubosphylum: Hexapoda Klase: Insecta Orden: Trichoptera Labawbanay: Hydropsychoidea Banay: Polycentropodidae Binomial nga ngaran Polycentropodidae An Polycentropodidae [1] in uska familia han Insecta. An Polycentropodidae in nahilalakip ha familia nga Hydropsychoidea, ordo nga Trichoptera, classis nga Insecta, punoan nga Arthropoda, ngan regnum nga Animalia. [1] An familia nga Polycentropodidae in naglalakip hin 660 ka mga species, sumala ha Catalogue of Life [1] . An kladograma hini sumala ha Catalogue of Life [1] : Hydropsychoidea   Polycentropodidae  Adectophylax Antillopsyche Cernotina Cyrnellus Cyrnodes Cyrnopsis Cyrnus Eodipseudopsis Eoneureclipsis Holocentropus Kambaitipsyche Neucentropus ...
            Read more