> With Maxima built from recent source (approximately Maxima 5.38),
> I get results that agree with what you expected

Thanks Robert, yes, I suspected the numerical integration
prematurely. A plot clearly shows that the culprit are the
real parts of the hyperbolic functions.

plot([tanh(exp(i*t)).real(), (exp(exp(i*t))/cosh(exp(i*t))-1).real()],t,0,2*pi)
The two functions are identical, the plot shows different functions.

> For realpart(tanh(exp(%i*t))/exp(%i*t*v)) I get:
> [...]
> Are you getting something different for that?

I get for (tanh(exp(i*t))/exp(i*t*v)).real()

-e^(imag_part(v)*real_part(t) + imag_part(t)*real_part(v))*
sin(imag_part(t)*imag_part(v) - real_part(t)*real_part(v))*
tan(e^(-imag_part(t))*sin(real_part(t)))/(tan(e^(-imag_part(t))*
sin(real_part(t)))^2*tanh(cos(real_part(t))*e^(-imag_part(t)))^2+1)+
cos(imag_part(t)*imag_part(v) - real_part(t)*real_part(v))*
e^(imag_part(v)*real_part(t) + imag_part(t)*real_part(v))*
tanh(cos(real_part(t))*e^(-imag_part(t)))/(tan(e^(-imag_part(t))*
sin(real_part(t)))^2*tanh(cos(real_part(t))*e^(-imag_part(t)))^2 + 1)

Cheers,
Peter

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