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

The function defined by $\csc x\equiv {1/\sin x}$, where $\sin x$ is the Sine. The Maclaurin Series of the cosecant function is

$\displaystyle \csc x$ $\textstyle =$ $\displaystyle {1\over x}+{\textstyle{1\over 6}}x+{\textstyle{7\over 360}}x^3+{\textstyle{31\over 15120}}x^5+\ldots$  
  $\textstyle \phantom{=}$ $\displaystyle +{(-1)^{n+1}2(2^{2n-1}-1)B_{2n}\over(2n)!}x^{2n-1}+\ldots,$  

where $B_{2n}$ is a Bernoulli Number.

See also Inverse Cosecant, Secant, Sine


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