I'm brand new to Mathematica and having to use it for my PDE class. One of my homework questions involves plotting the first few terms of the Fourier series of a solution to a PDE, but the eigenvalues are positive solutions to an equation, for example $tan(p)=p$. How can I get a sequence $p_n$ where $p_n$ is the $n^{th}$ positive solution to the equation?

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    – Michael E2
    Commented Oct 6, 2017 at 18:19
  • $\begingroup$ Related/duplicate: mathematica.stackexchange.com/questions/65896/… $\endgroup$
    – Michael E2
    Commented Oct 6, 2017 at 19:13

1 Answer 1


Do you mean something like this?

nmax = 10;
tlist = t /. Table[FindRoot[Tan[t] == t, {t, -0.1 + Pi n}], {n, 0, nmax}];
 Plot[{Tan[t], t}, {t, -nmax Pi, nmax Pi}, PlotRange -> All],
 ListPlot[{tlist, tlist}\[Transpose], PlotStyle -> Black]

Otherwise, you should be a bit more specific...

enter image description here

  • $\begingroup$ You can also use Epilog: nmax = 10; tlist = Select[ t /. Table[FindRoot[Tan[t] == t, {t, -0.1 + Pi n}], {n, 0, nmax}], 0 < # < nmax Pi &] Plot[{Tan[t], t}, {t, 0, nmax Pi}, PlotRange -> All, Epilog -> {Red, AbsolutePointSize[4], Point[{#, #} & /@ tlist]}, PlotLegends -> "Expressions"] $\endgroup$
    – Bob Hanlon
    Commented Oct 6, 2017 at 17:30
  • $\begingroup$ No, I need to be able to evaluate an expression involving the nth solution $\endgroup$
    – Zachary F
    Commented Oct 6, 2017 at 17:31
  • $\begingroup$ @ZacharyF. tlist is a list, in order, of the roots. That sounds like what you want. $\endgroup$
    – march
    Commented Oct 6, 2017 at 17:35

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