$frac1p+frac1q=1$ vs $sum_n=0^infty frac1p^n=q$

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











up vote
6
down vote

favorite
4












It just occurred to me that conjugate exponents, i.e. $p,qin(1,+infty)$ such that $$frac1p+frac1q =1$$
also satisfy the relations:



  • $sum_n=0^infty frac1p^n=q;$

  • $sum_n=0^infty frac1q^n=p.$

I never saw this fact used in the study of $L^p$ spaces... does anyone know any application of these relations in that context?







share|cite|improve this question























    up vote
    6
    down vote

    favorite
    4












    It just occurred to me that conjugate exponents, i.e. $p,qin(1,+infty)$ such that $$frac1p+frac1q =1$$
    also satisfy the relations:



    • $sum_n=0^infty frac1p^n=q;$

    • $sum_n=0^infty frac1q^n=p.$

    I never saw this fact used in the study of $L^p$ spaces... does anyone know any application of these relations in that context?







    share|cite|improve this question





















      up vote
      6
      down vote

      favorite
      4









      up vote
      6
      down vote

      favorite
      4






      4





      It just occurred to me that conjugate exponents, i.e. $p,qin(1,+infty)$ such that $$frac1p+frac1q =1$$
      also satisfy the relations:



      • $sum_n=0^infty frac1p^n=q;$

      • $sum_n=0^infty frac1q^n=p.$

      I never saw this fact used in the study of $L^p$ spaces... does anyone know any application of these relations in that context?







      share|cite|improve this question











      It just occurred to me that conjugate exponents, i.e. $p,qin(1,+infty)$ such that $$frac1p+frac1q =1$$
      also satisfy the relations:



      • $sum_n=0^infty frac1p^n=q;$

      • $sum_n=0^infty frac1q^n=p.$

      I never saw this fact used in the study of $L^p$ spaces... does anyone know any application of these relations in that context?









      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









      asked Aug 7 at 21:27









      Bob

      1,489522




      1,489522

























          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',
          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%2f2875420%2ffrac1p-frac1q-1-vs-sum-n-0-infty-frac1pn-q%23new-answer', 'question_page');

          );

          Post as a guest



































          active

          oldest

          votes













          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes










           

          draft saved


          draft discarded


























           


          draft saved


          draft discarded














          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2875420%2ffrac1p-frac1q-1-vs-sum-n-0-infty-frac1pn-q%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?