# Periodic piecewise function

Posted 10 years ago
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 I have some very simple questions about how to define a periodic function in Mathematica. I've never used Mathematica before so please forgive my ignorance.What I need to do is graph and obtain the Fourier series for a 2*Pi-periodic function. My function is defined as follows:exp(x) when -pi < x < picosh(pi) when x = -pi or x = piI told this to Mathematica this way:f[x_] := Piecewise[{{Exp[x], -Pi < x < Pi}, {Cosh[x],     x == -Pi || x == Pi}}]I think it worked properly because when I evaluate the function I get the appropriate results.Now the problem is I need to extend this definition to the whole real number line, taking into account that f(x+2pi) = f(x). I tried to do this several ways, but none of them worked and I couldn't figure out a solution.Another issue is how to plot this showing the points (n*pi, cosh(n*pi)). When I plot the function it shows the line for exp(x) but nothing for cosh(x), and I need the dots to be seen. Any help would be appreciated.
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Posted 10 years ago
 All the solutions worked like a charm, just like I wanted. Thank you very much!
Posted 10 years ago
 Another way is thinking recursively! f[x_] := Which[x > Pi, f[x - 2*Pi],               x < -Pi, f[x + 2*Pi],              -Pi < x < Pi, Exp[x],               x == -Pi || x == Pi, Cosh[x]  ]
Posted 10 years ago
 For the periodic continuation, could try g[x_] := f[Mod[x, 2 Pi, -Pi]] and use Epilog to add the discrete points to the plot.EDIT: Too slow, Szabolcs already answered :-)
Posted 10 years ago
 Would defining your function asExp@Mod[x, 2 Pi, -Pi]work for your purposes?  It will work for plotting (except for the Cosh part, but that value is taken only in separate points).