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:<math>\coth x = \frac {1} {x} + \frac {x} {3} - \frac {x^3} {45} + \frac {2x^5} {945} + \cdots = </math>
:<math>\operatorname {sech} x = 1 - \frac {x^2} {2} + \frac {5x^4} {24} - \frac {61x^6} {720} + \cdots = </math>
:<math>\operatorname {csch} x = \frac {1} {x} - \frac {x} {6} +\frac {7x^3} {360} -\frac {31x^5} {15120} + \cdots = </math>
where
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