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: <math>\operatorname{tanhc} z \approx \left(1-\frac{1}{3} z^2 + \frac {2}{15} z^4 - \frac {17}{315} z^6 + \frac {62}{2835} z^8 - \frac {1382}{155925} z^{10} + \frac {21844}{6081075} z^{12} - \frac {929569}{638512875} z^{14}+O(z^{16}) \right)</math>
:<math>\int _{0}^{z}\!{\frac {\tanh \left( x \right) }{x}}{dx}=(z-{\frac {1}{
9}}{z}^{3}+{\frac {2}{75}}{z}^{5}-{\frac {17}{2205}}{z}^{7}+{\frac {62
}{25515}}{z}^{9}-{\frac {1382}{1715175}}{z}^{11}+O \left( {z}^{13} \right) )</math>
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