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I have a recursion relation defined as

Clear[f];
f[x_] := 0 /; 0 <= x < π/3;
f[x_] := x - π/3 /; π/3 <= x < 2 π/3;
f[x_] := f[x - 2 π/3] + π/3 /; x >= 2 π/3;
f[x_] := -f[π/3 - x] /; x < 0;

Plot[f[x], {x,-2Pi,2Pi}, Ticks->{Range[-2π,2π,π/2], Automatic}]

enter image description here

I'm unsure of where to go from here to find the solution. RSolve seems doesn't worked.

How to use Mathematica to find it?

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    $\begingroup$ Maybe h[x_] := Max[Mod[x, 2/3 \[Pi]] - \[Pi]/3, 0] + Quotient[x, 2/3 \[Pi]] \[Pi]/3 ? $\endgroup$ Jan 9, 2018 at 8:16
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    $\begingroup$ ... Is this a math question or a Mathematica question? The answers here give "the mathematical result", not "how to use Mathematica to find it". $\endgroup$
    – user202729
    Jan 9, 2018 at 9:51

1 Answer 1

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f2[x_] := If[EvenQ[#], # π/6, (# - 1) π /6 + #2] & @@ QuotientRemainder[x, π/3];

Plot[{f2[x], f[x]}, {x, -2 π, 2 π}, 
 Ticks -> {Range[-2 π, 2 π, π/3], Automatic},  
 PlotStyle -> {Directive[Opacity[.7], Thickness[.01], Red], 
   Directive[Black, Dashed]}, PlotLegends -> "Expressions"]

enter image description here

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  • $\begingroup$ Yes... but how did you find this function? $\endgroup$ Jan 10, 2018 at 1:03
  • $\begingroup$ @DavidG.Stork, by squinting (really hard, unfortunately):) $\endgroup$
    – kglr
    Jan 10, 2018 at 1:36

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