The haversine, also called the haversed sine, is a little-used entire trigonometric function defined by
where 
is the versine,
is the cosine,
and 
is the sine.
The haversine is implemented in the Wolfram Language as Haversine[z].
The haversine can be extended to the complex plane as illustrated above.
Its derivative is given by
 |
(4) |
and its indefinite integral by
 |
(5) |
It has Maclaurin series
See also
Covercosine, Coversine, Excosecant, Exsecant, Hacoversine, Havercosine, Vercosine, Versine
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References
Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 78, 1972.Smart, W. M. Text-Book on Spherical Astronomy, 6th ed. Cambridge, England: Cambridge University Press, p. 18, 1960.
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Cite this as:
Weisstein, Eric W. "Haversine." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Haversine.html