O17-089
> restart;
> f:=sum(x^n/(1+x^(2*n)),n=0..infinity);

                            infinity
                             -----        n
                              \          x
                       f :=    )     ----------
                              /           (2 n)
                             -----   1 + x
                             n = 0

> plot(f,x=-10..10);

> assume(x>0 and x<1);int(1/cosh(-t*ln(x)),t=0..infinity);

                                    Pi
                             -1/2 ------
                                  ln(x~)

> limit(f,x=-1);

                              undefined

> assume(x>0 and x<1);int(1/cosh(-(2*t+1)*ln(x)),t=0..infinity);

                               arctan(x~)
                             - ----------
                                 ln(x~)

>