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)