usig mobius inversion to solve this problem?

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











up vote
0
down vote

favorite
1












let be the functional equation



$$ g(x) = f(x/2)log(2) +f(x/3)log(3)+ f(x/4)log(4).... $$



where log is the logarithm in basis 'e'



how could i use mobius inversion formula to obtain the function$ f(x)$ from the



equation above ?



i believe that if we call $$ frac1zeta ' (s) = sum_n=1^infty fracb(n)n^s $$



so $$ f(x)= g(x)b(1)+g(x/2)b(2)+g(x/3)b(3) $$










share|cite|improve this question

























    up vote
    0
    down vote

    favorite
    1












    let be the functional equation



    $$ g(x) = f(x/2)log(2) +f(x/3)log(3)+ f(x/4)log(4).... $$



    where log is the logarithm in basis 'e'



    how could i use mobius inversion formula to obtain the function$ f(x)$ from the



    equation above ?



    i believe that if we call $$ frac1zeta ' (s) = sum_n=1^infty fracb(n)n^s $$



    so $$ f(x)= g(x)b(1)+g(x/2)b(2)+g(x/3)b(3) $$










    share|cite|improve this question























      up vote
      0
      down vote

      favorite
      1









      up vote
      0
      down vote

      favorite
      1






      1





      let be the functional equation



      $$ g(x) = f(x/2)log(2) +f(x/3)log(3)+ f(x/4)log(4).... $$



      where log is the logarithm in basis 'e'



      how could i use mobius inversion formula to obtain the function$ f(x)$ from the



      equation above ?



      i believe that if we call $$ frac1zeta ' (s) = sum_n=1^infty fracb(n)n^s $$



      so $$ f(x)= g(x)b(1)+g(x/2)b(2)+g(x/3)b(3) $$










      share|cite|improve this question













      let be the functional equation



      $$ g(x) = f(x/2)log(2) +f(x/3)log(3)+ f(x/4)log(4).... $$



      where log is the logarithm in basis 'e'



      how could i use mobius inversion formula to obtain the function$ f(x)$ from the



      equation above ?



      i believe that if we call $$ frac1zeta ' (s) = sum_n=1^infty fracb(n)n^s $$



      so $$ f(x)= g(x)b(1)+g(x/2)b(2)+g(x/3)b(3) $$







      mobius-inversion






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Sep 2 at 10:54









      Jose Garcia

      4,02511235




      4,02511235

























          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%2f2902591%2fusig-mobius-inversion-to-solve-this-problem%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%2f2902591%2fusig-mobius-inversion-to-solve-this-problem%23new-answer', 'question_page');

          );

          Post as a guest













































































          這個網誌中的熱門文章

          Is there any way to eliminate the singular point to solve this integral by hand or by approximations?

          Why am i infinitely getting the same tweet with the Twitter Search API?

          Amount of Number Combinations to Reach a Sum of 10 With Integers 1-9 Using 2 or More Integers [closed]