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Plot special functions real and imaginary part?

Azad Kaygun

Posted 8 years ago

Consider the following code: 0F1[;1;jpi/2x]e^j2pix x[-pi/2,+pi/2] The task is to visualize the real and imaginary part here is how i tried it what has to be different?besides i need the first three derivatives it didnt work like that Grid[ Partition[ Table[ Plot[ Evaluate[{Re[ D[Hypergeometric0F1[ 1, (\[ImaginaryJ]\[Pi]/2x)E^j2\[Pi]x], {x, i}]], Im[D[ Hypergeometric0F1[ 1, (\[ImaginaryJ]\[Pi]/2x)E^j2\[Pi]x], {x, i}]]}], {x, -2/\[Pi], 2/\[Pi]}, PlotRange -> Automatic, Frame -> True, GridLines -> Automatic, AspectRatio -> 1, FrameLabel -> {"x", StringForm[ "\!\(\SubscriptBox[\(\[InvisiblePrefixScriptBase]\), \(0\)]\)\ \!\(\SubscriptBox[OverscriptBox[\(F\), \(~\)], \(1\)]\)^(``)(\ \[ImaginaryJ]\[Pi]/2x)\!\(\SuperscriptBox[\(\[ExponentialE]\), \ \(j2\[Pi]x\)]\)"]}, PlotLegends -> Placed[{"Re", "Im"}, {Center, Top}], ImageSize -> 300], {i, 0, 3}], 2], Frame -> All] Attachments:

Consider the following code:

0F1[;1;j*pi/2x]*e^j2*pi*x
x[-pi/2,+pi/2]

The task is to visualize the real and imaginary part here is how i tried it what has to be different?besides i need the first three derivatives it didnt work like that

Grid[
 Partition[
  Table[
   Plot[
    Evaluate[{Re[
       D[Hypergeometric0F1[
         1, (\[ImaginaryJ]*\[Pi]/2*x)*E^j2\[Pi]x], {x, i}]],
      Im[D[
        Hypergeometric0F1[
         1, (\[ImaginaryJ]*\[Pi]/2*x)*E^j2\[Pi]x], {x, i}]]}],
    {x, -2/\[Pi], 2/\[Pi]},
    PlotRange -> Automatic,
    Frame -> True,
    GridLines -> Automatic,
    AspectRatio -> 1,
    FrameLabel -> {"x", 
      StringForm[
       "\!\(\*SubscriptBox[\(\[InvisiblePrefixScriptBase]\), \(0\)]\)\
\!\(\*SubscriptBox[OverscriptBox[\(F\), \(~\)], \(1\)]\)^(``)(\
\[ImaginaryJ]*\[Pi]/2*x)*\!\(\*SuperscriptBox[\(\[ExponentialE]\), \
\(j2\[Pi]x\)]\)"]},
    PlotLegends -> Placed[{"Re", "Im"}, {Center, Top}],
    ImageSize -> 300], {i, 0, 3}], 2], Frame -> All]

POSTED BY: Azad Kaygun

3 Replies

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Udo Krause

Udo Krause, NOrganization

Posted 8 years ago

Had you used the I to denote the imaginary unit (instead of the `j` you took, which is okay only in comments), it had worked like a charme as seen here

POSTED BY: Udo Krause

Murray Eisenberg

Murray Eisenberg, University of Massachusetts Amherst

Posted 8 years ago

Please post code in text form that readers can directly copy and paste into a notebook! And then add the graphic output by using this site's image tool icon.

POSTED BY: Murray Eisenberg

Udo Krause

Udo Krause, NOrganization

Posted 8 years ago

Grid[ Partition[ Table[ Plot[ Evaluate[{Re[ D[Hypergeometric0F1[1, (I\[Pi]/2x)Exp[I 2 \[Pi] x]], {x, i}]], Im[D[ Hypergeometric0F1[1, (I\[Pi]/2x)Exp[I 2 \[Pi] x]], {x, i}]]}], {x, -2/\[Pi], 2/\[Pi]}, PlotRange -> Automatic, Frame -> True, GridLines -> Automatic, AspectRatio -> 1, FrameLabel -> {"x", StringForm[ "\!\(\SubscriptBox[\(\[InvisiblePrefixScriptBase]\), \(0\)]\)\ \!\(\SubscriptBox[OverscriptBox[\(F\), \(~\)], \(1\)]\)^(``)(\ \[ImaginaryJ]\[Pi]/2x)\!\(\SuperscriptBox[\(\[ExponentialE]\), \ \(j2\[Pi]x\)]\)"]}, PlotLegends -> Placed[{"Re", "Im"}, {Center, Top}], ImageSize -> 300], {i, 0, 3}], 2], Frame -> All] Many thanks for your kind hint.

Grid[
 Partition[
  Table[
   Plot[
    Evaluate[{Re[
       D[Hypergeometric0F1[1, (I*\[Pi]/2*x)*Exp[I 2 \[Pi] x]], {x, 
         i}]],
      Im[D[
        Hypergeometric0F1[1, (I*\[Pi]/2*x)*Exp[I 2 \[Pi] x]], {x, 
         i}]]}],
    {x, -2/\[Pi], 2/\[Pi]},
    PlotRange -> Automatic,
    Frame -> True,
    GridLines -> Automatic,
    AspectRatio -> 1,
    FrameLabel -> {"x", 
      StringForm[
       "\!\(\*SubscriptBox[\(\[InvisiblePrefixScriptBase]\), \(0\)]\)\
\!\(\*SubscriptBox[OverscriptBox[\(F\), \(~\)], \(1\)]\)^(``)(\
\[ImaginaryJ]*\[Pi]/2*x)*\!\(\*SuperscriptBox[\(\[ExponentialE]\), \
\(j2\[Pi]x\)]\)"]},
    PlotLegends -> Placed[{"Re", "Im"}, {Center, Top}],
    ImageSize -> 300], {i, 0, 3}], 2], Frame -> All]

Many thanks for your kind hint.

POSTED BY: Udo Krause

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