Fourier analysis notation - Sh and Ch

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











up vote
0
down vote

favorite












I reading something dealing with Fourier analysis and don't know what "Sh" and "Ch" indicate. Thanks!










share|cite|improve this question



















  • 2




    My money's on hyperbolic sine and cosine.
    – user1337
    Jun 21 '15 at 8:45










  • This was how we used to write $sinh$ and $cosh$ in France when I was young (looong time ago).
    – Claude Leibovici
    Jun 21 '15 at 8:47










  • Also written $sinh$ and $cosh$, and Hyp Sin, Hyp Cos on some calculators.
    – Yves Daoust
    Jun 21 '15 at 8:47















up vote
0
down vote

favorite












I reading something dealing with Fourier analysis and don't know what "Sh" and "Ch" indicate. Thanks!










share|cite|improve this question



















  • 2




    My money's on hyperbolic sine and cosine.
    – user1337
    Jun 21 '15 at 8:45










  • This was how we used to write $sinh$ and $cosh$ in France when I was young (looong time ago).
    – Claude Leibovici
    Jun 21 '15 at 8:47










  • Also written $sinh$ and $cosh$, and Hyp Sin, Hyp Cos on some calculators.
    – Yves Daoust
    Jun 21 '15 at 8:47













up vote
0
down vote

favorite









up vote
0
down vote

favorite











I reading something dealing with Fourier analysis and don't know what "Sh" and "Ch" indicate. Thanks!










share|cite|improve this question















I reading something dealing with Fourier analysis and don't know what "Sh" and "Ch" indicate. Thanks!







notation fourier-analysis






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jun 21 '15 at 10:07









wythagoras

21.4k442103




21.4k442103










asked Jun 21 '15 at 8:44









wellfedgremlin

367119




367119







  • 2




    My money's on hyperbolic sine and cosine.
    – user1337
    Jun 21 '15 at 8:45










  • This was how we used to write $sinh$ and $cosh$ in France when I was young (looong time ago).
    – Claude Leibovici
    Jun 21 '15 at 8:47










  • Also written $sinh$ and $cosh$, and Hyp Sin, Hyp Cos on some calculators.
    – Yves Daoust
    Jun 21 '15 at 8:47













  • 2




    My money's on hyperbolic sine and cosine.
    – user1337
    Jun 21 '15 at 8:45










  • This was how we used to write $sinh$ and $cosh$ in France when I was young (looong time ago).
    – Claude Leibovici
    Jun 21 '15 at 8:47










  • Also written $sinh$ and $cosh$, and Hyp Sin, Hyp Cos on some calculators.
    – Yves Daoust
    Jun 21 '15 at 8:47








2




2




My money's on hyperbolic sine and cosine.
– user1337
Jun 21 '15 at 8:45




My money's on hyperbolic sine and cosine.
– user1337
Jun 21 '15 at 8:45












This was how we used to write $sinh$ and $cosh$ in France when I was young (looong time ago).
– Claude Leibovici
Jun 21 '15 at 8:47




This was how we used to write $sinh$ and $cosh$ in France when I was young (looong time ago).
– Claude Leibovici
Jun 21 '15 at 8:47












Also written $sinh$ and $cosh$, and Hyp Sin, Hyp Cos on some calculators.
– Yves Daoust
Jun 21 '15 at 8:47





Also written $sinh$ and $cosh$, and Hyp Sin, Hyp Cos on some calculators.
– Yves Daoust
Jun 21 '15 at 8:47











1 Answer
1






active

oldest

votes

















up vote
0
down vote













The hyperbolic functions are the "real" counterparts of the ordinary trigonometric ones.



$$textch(x)=cosh(x)=frace^x+e^-x2leftrightarrow cos(x)=frace^ix+e^-ix2,$$



$$textsh(x)=sinh(x)=frace^x-e^-x2leftrightarrow sin(x)=frace^ix-e^-ix2i.$$



They are odd and even linear combinations of the exponential, so they easily appear with the latter.



Their name stems form the relation
$$c^2-s^2=1$$ that corresponds to an hyperbola, to be compared to



$$c^2+s^2=1$$ for the circular functions.






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%2f1333475%2ffourier-analysis-notation-sh-and-ch%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
    0
    down vote













    The hyperbolic functions are the "real" counterparts of the ordinary trigonometric ones.



    $$textch(x)=cosh(x)=frace^x+e^-x2leftrightarrow cos(x)=frace^ix+e^-ix2,$$



    $$textsh(x)=sinh(x)=frace^x-e^-x2leftrightarrow sin(x)=frace^ix-e^-ix2i.$$



    They are odd and even linear combinations of the exponential, so they easily appear with the latter.



    Their name stems form the relation
    $$c^2-s^2=1$$ that corresponds to an hyperbola, to be compared to



    $$c^2+s^2=1$$ for the circular functions.






    share|cite|improve this answer


























      up vote
      0
      down vote













      The hyperbolic functions are the "real" counterparts of the ordinary trigonometric ones.



      $$textch(x)=cosh(x)=frace^x+e^-x2leftrightarrow cos(x)=frace^ix+e^-ix2,$$



      $$textsh(x)=sinh(x)=frace^x-e^-x2leftrightarrow sin(x)=frace^ix-e^-ix2i.$$



      They are odd and even linear combinations of the exponential, so they easily appear with the latter.



      Their name stems form the relation
      $$c^2-s^2=1$$ that corresponds to an hyperbola, to be compared to



      $$c^2+s^2=1$$ for the circular functions.






      share|cite|improve this answer
























        up vote
        0
        down vote










        up vote
        0
        down vote









        The hyperbolic functions are the "real" counterparts of the ordinary trigonometric ones.



        $$textch(x)=cosh(x)=frace^x+e^-x2leftrightarrow cos(x)=frace^ix+e^-ix2,$$



        $$textsh(x)=sinh(x)=frace^x-e^-x2leftrightarrow sin(x)=frace^ix-e^-ix2i.$$



        They are odd and even linear combinations of the exponential, so they easily appear with the latter.



        Their name stems form the relation
        $$c^2-s^2=1$$ that corresponds to an hyperbola, to be compared to



        $$c^2+s^2=1$$ for the circular functions.






        share|cite|improve this answer














        The hyperbolic functions are the "real" counterparts of the ordinary trigonometric ones.



        $$textch(x)=cosh(x)=frace^x+e^-x2leftrightarrow cos(x)=frace^ix+e^-ix2,$$



        $$textsh(x)=sinh(x)=frace^x-e^-x2leftrightarrow sin(x)=frace^ix-e^-ix2i.$$



        They are odd and even linear combinations of the exponential, so they easily appear with the latter.



        Their name stems form the relation
        $$c^2-s^2=1$$ that corresponds to an hyperbola, to be compared to



        $$c^2+s^2=1$$ for the circular functions.







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited Jun 22 '15 at 10:05

























        answered Jun 21 '15 at 8:55









        Yves Daoust

        114k665209




        114k665209



























             

            draft saved


            draft discarded















































             


            draft saved


            draft discarded














            StackExchange.ready(
            function ()
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f1333475%2ffourier-analysis-notation-sh-and-ch%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?