Inverse Trigonometric Functions -Inverse Haversine

The inverse haversine function  is defined by

(1)

The inverse haversine is implemented in the Wolfram Language as InverseHaversine[z].

It has derivative

(2)

and indefinite integral

(3)

where  is a constant of integration.

The inverse haversine has the series expansion

			(4)
			(5)

(OEIS A143581 and A143582).

REFERENCES:

Sloane, N. J. A. Sequences A143581 and A143582 in "The On-Line Encyclopedia of Integer Sequences."