Under what condition can we analytically continue an equation?

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











up vote
2
down vote

favorite












Suppose we have an equation
$$(partial_x^2+bpartial_x+h(x))f(x)=g(x)$$
which we known is satisfied for real $x$.



Under what conditions, can we continue it to
$$(partial_z^2+bpartial_z+h(z))f(z)=g(z)$$
for complex $z$?







share|cite|improve this question
























    up vote
    2
    down vote

    favorite












    Suppose we have an equation
    $$(partial_x^2+bpartial_x+h(x))f(x)=g(x)$$
    which we known is satisfied for real $x$.



    Under what conditions, can we continue it to
    $$(partial_z^2+bpartial_z+h(z))f(z)=g(z)$$
    for complex $z$?







    share|cite|improve this question






















      up vote
      2
      down vote

      favorite









      up vote
      2
      down vote

      favorite











      Suppose we have an equation
      $$(partial_x^2+bpartial_x+h(x))f(x)=g(x)$$
      which we known is satisfied for real $x$.



      Under what conditions, can we continue it to
      $$(partial_z^2+bpartial_z+h(z))f(z)=g(z)$$
      for complex $z$?







      share|cite|improve this question












      Suppose we have an equation
      $$(partial_x^2+bpartial_x+h(x))f(x)=g(x)$$
      which we known is satisfied for real $x$.



      Under what conditions, can we continue it to
      $$(partial_z^2+bpartial_z+h(z))f(z)=g(z)$$
      for complex $z$?









      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Aug 22 at 9:34









      Wein Eld

      207111




      207111

























          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%2f2890848%2funder-what-condition-can-we-analytically-continue-an-equation%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%2f2890848%2funder-what-condition-can-we-analytically-continue-an-equation%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?