Hyperbolic Cosecant

The hyperbolic cosecant is defined as

$$\mathop{\rm csch}\nolimits x\equiv {1\over\sinh x} = {2\over e^x-e^{-x}}.$$

See also Bernoulli Number, Bipolar Coordinates, Bipolar Cylindrical Coordinates, Cosecant, Helmholtz Differential Equation--Toroidal Coordinates, Hyperbolic Sine, Poinsot's Spirals, Surface of Revolution, Toroidal Function

References

Abramowitz, M. and Stegun, C. A. (Eds.). ``Hyperbolic Functions.'' §4.5 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 83-86, 1972.

Spanier, J. and Oldham, K. B. ``The Hyperbolic Secant $\mathop{\rm sech}\nolimits (x)$ and Cosecant $\mathop{\rm csch}\nolimits (x)$ Functions.'' Ch. 29 in An Atlas of Functions. Washington, DC: Hemisphere, pp. 273-278, 1987.