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

The function defined by $\sec x\equiv {1/\cos x}$, where $\cos x$ is the Cosine. The Maclaurin Series of the secant is

\sec x &=& {(-1)^nE_{2n}\over (2n)!}x^{2n}\\
...extstyle{61\over 720}}x^6+{\textstyle{277\over 8064}}x^8+\ldots,

where $E_{2n}$ is an Euler Number.

See also Alternating Permutation, Cosecant, Cosine, Euler Number, Exsecant, Inverse Secant


Abramowitz, M. and Stegun, C. A. (Eds.). ``Circular Functions.'' §4.3 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 71-79, 1972.

Spanier, J. and Oldham, K. B. ``The Secant $\sec(x)$ and Cosecant $\csc(x)$ Functions.'' Ch. 33 in An Atlas of Functions. Washington, DC: Hemisphere, pp. 311-318, 1987.

© 1996-9 Eric W. Weisstein