Haversine

The haversine, also called the haversed sine, is a little-used entire trigonometric function defined by

			(1)
			(2)
			(3)

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

			(6)
			(7)

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.