Does version 11 have this bug in FourierSeries?

Bug introduced in 7.0.1 or earlier and persisting through 11.1

I am using version 10.0 with Apple OS X. Consider the following.

f[t_]:=1/(1+25.0*(t-0.3)^2);
Plot[f[t],{t,-1,1}]


Below FourierSeries retruns the wrong series.

WrongSeries[t_]=Chop@Expand@ExpToTrig@FourierSeries[
f[t],t,4,FourierParameters->{1,\[Pi]}];
Plot[WrongSeries[t],{t,-1,1},
PlotLabel->Style["The Wrong Truncated Fourier Series",14,Bold]]


Does Version 11 also have this problem?

-----EDIT-----

I can derive the right series using a combination of FourierCosSeries and FourierSinSeries.

RightSeries[t_]=Expand[(
FourierCosSeries[f[t]+f[-t],t,4,FourierParameters->{1,\[Pi]}]+
FourierSinSeries[f[t]-f[-t],t,7,FourierParameters->{1,\[Pi]}])/2
];
Plot[{f[t],RightSeries[t]},{t,-1,1},
PlotLegends->{"g[t]","Truncated Fourier Series"}]


• Hi; I run 11.0 on linux and I get that too. – bobbym Mar 11 '17 at 19:24
• Same with 11.0 on Windows. Image – jjc385 Mar 11 '17 at 19:28
• Sadly, the same bug even with version 7.0.1 on Win7x64. – innaiz Mar 13 '17 at 22:08
• I can confirm that the bug is present in MMA 11.1.0. – user58955 Mar 23 '17 at 17:48

f[t_]:=1/(1+25.0*(t-0.3)^2);