\[\coth x = \frac{{{e^{2x}} + 1}}{{{e^{2x}} - 1}} = \frac{1}{x} + \frac{{\frac{1}{{1 \cdot 3}}}}{{\frac{1}{x} + \frac{{\frac{1}{{3 \cdot 5}}}}{{\frac{1}{x} + \frac{{\frac{1}{{5 \cdot 7}}}}{{\frac{1}{x} + ...}}}}}}.\]