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.Referenced on Wolfram|Alpha
Haversine
Cite this as:
Weisstein, Eric W. "Haversine." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Haversine.html
Subject classifications