This Jupyter/SageMath notebook is relative to the lectures Geometry and physics of black holes.
%display latex
integrate(sqrt(1-x^2), x)
f(x) = (sqrt(1-x^2) + asin(x)/x)/2
f(x)
taylor(f(x), x, 0, 5)
g = plot(f(x), (x, -1, 1), thickness=2, gridlines='major',
axes_labels=[r'$h$', r'$L_{(p,q)}(\mathscr{L}_h)/T$'],
fontsize=14)
g
g.save('geo_timelike_length_h.pdf')