# How can I create a sequence of solutions to an equation?

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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Do you mean something like this?

nmax = 10;
tlist = t /. Table[FindRoot[Tan[t] == t, {t, -0.1 + Pi n}], {n, 0, nmax}];
Show[
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...

• 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"] – Bob Hanlon Oct 6 '17 at 17:30
• No, I need to be able to evaluate an expression involving the nth solution – Zachary F Oct 6 '17 at 17:31
• @ZacharyF. tlist is a list, in order, of the roots. That sounds like what you want. – march Oct 6 '17 at 17:35