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Hyperbolic Secant


\begin{figure}\begin{center}\BoxedEPSF{SechReIm.epsf scaled 700}\end{center}\end{figure}

The hyperbolic secant is defined as

\mathop{\rm sech}\nolimits x\equiv {1\over\cosh x} = {2\over e^x+e^{-x}}.

It has a Maximum at $x=0$ and inflection points at $x=\pm\mathop{\rm sech}\nolimits ^{-1}(1/\sqrt{2}\,)\approx 0.881374$.

See also Benson's Formula, Catenary, Catenoid, Euler Number, Hyperbolic Cosine, Oblate Spheroidal Coordinates, Pseudosphere, Secant, Surface of Revolution, Tractrix, Tractroid


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.

© 1996-9 Eric W. Weisstein