Kernel of Hankel Transform

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











up vote
0
down vote

favorite












I need to solve a cylindrical diffusion problem that is defined in $[1,infty]$. I would like to use Hankel Transform that has is defined on $[0,infty]$. So in order to apply Hankel transform in my case, do I need to change the Kernel of the Transformation.







share|cite|improve this question






















  • You probably have a condition at $r=1$. So your transform should be tailored to that condition.
    – DisintegratingByParts
    Aug 9 at 17:38














up vote
0
down vote

favorite












I need to solve a cylindrical diffusion problem that is defined in $[1,infty]$. I would like to use Hankel Transform that has is defined on $[0,infty]$. So in order to apply Hankel transform in my case, do I need to change the Kernel of the Transformation.







share|cite|improve this question






















  • You probably have a condition at $r=1$. So your transform should be tailored to that condition.
    – DisintegratingByParts
    Aug 9 at 17:38












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I need to solve a cylindrical diffusion problem that is defined in $[1,infty]$. I would like to use Hankel Transform that has is defined on $[0,infty]$. So in order to apply Hankel transform in my case, do I need to change the Kernel of the Transformation.







share|cite|improve this question














I need to solve a cylindrical diffusion problem that is defined in $[1,infty]$. I would like to use Hankel Transform that has is defined on $[0,infty]$. So in order to apply Hankel transform in my case, do I need to change the Kernel of the Transformation.









share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Aug 8 at 18:42









Javi

2,1711725




2,1711725










asked Aug 8 at 18:07









Three Phi

55




55











  • You probably have a condition at $r=1$. So your transform should be tailored to that condition.
    – DisintegratingByParts
    Aug 9 at 17:38
















  • You probably have a condition at $r=1$. So your transform should be tailored to that condition.
    – DisintegratingByParts
    Aug 9 at 17:38















You probably have a condition at $r=1$. So your transform should be tailored to that condition.
– DisintegratingByParts
Aug 9 at 17:38




You probably have a condition at $r=1$. So your transform should be tailored to that condition.
– DisintegratingByParts
Aug 9 at 17:38










1 Answer
1






active

oldest

votes

















up vote
1
down vote













Yes, you do.



In general, the Bessel solutions to the boundary value problem require that the function remains finite at r = 0.



If your domain does not include r = 0 (and yours does not!) then you need to use a linear combination of Bessel functions of the first, and second kind.



A bit of Googling will help you to get a good idea about how to go about this. For example, "Theory and Operational Rules for the Discrete Hankel Transform" is a very nice paper which attempts to put the DHT on equal footing with the discrete Fourier transform.






share|cite|improve this answer




















    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%2f2876397%2fkernel-of-hankel-transform%23new-answer', 'question_page');

    );

    Post as a guest






























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    1
    down vote













    Yes, you do.



    In general, the Bessel solutions to the boundary value problem require that the function remains finite at r = 0.



    If your domain does not include r = 0 (and yours does not!) then you need to use a linear combination of Bessel functions of the first, and second kind.



    A bit of Googling will help you to get a good idea about how to go about this. For example, "Theory and Operational Rules for the Discrete Hankel Transform" is a very nice paper which attempts to put the DHT on equal footing with the discrete Fourier transform.






    share|cite|improve this answer
























      up vote
      1
      down vote













      Yes, you do.



      In general, the Bessel solutions to the boundary value problem require that the function remains finite at r = 0.



      If your domain does not include r = 0 (and yours does not!) then you need to use a linear combination of Bessel functions of the first, and second kind.



      A bit of Googling will help you to get a good idea about how to go about this. For example, "Theory and Operational Rules for the Discrete Hankel Transform" is a very nice paper which attempts to put the DHT on equal footing with the discrete Fourier transform.






      share|cite|improve this answer






















        up vote
        1
        down vote










        up vote
        1
        down vote









        Yes, you do.



        In general, the Bessel solutions to the boundary value problem require that the function remains finite at r = 0.



        If your domain does not include r = 0 (and yours does not!) then you need to use a linear combination of Bessel functions of the first, and second kind.



        A bit of Googling will help you to get a good idea about how to go about this. For example, "Theory and Operational Rules for the Discrete Hankel Transform" is a very nice paper which attempts to put the DHT on equal footing with the discrete Fourier transform.






        share|cite|improve this answer












        Yes, you do.



        In general, the Bessel solutions to the boundary value problem require that the function remains finite at r = 0.



        If your domain does not include r = 0 (and yours does not!) then you need to use a linear combination of Bessel functions of the first, and second kind.



        A bit of Googling will help you to get a good idea about how to go about this. For example, "Theory and Operational Rules for the Discrete Hankel Transform" is a very nice paper which attempts to put the DHT on equal footing with the discrete Fourier transform.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Aug 8 at 20:01









        user109527

        657




        657






















             

            draft saved


            draft discarded


























             


            draft saved


            draft discarded














            StackExchange.ready(
            function ()
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2876397%2fkernel-of-hankel-transform%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?