Haversine
The haversine, also called the haversed sine, is a little-used entire trigonometric function defined by
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(1)
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(2)
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(3)
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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
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(4)
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and its indefinite integral by
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(5)
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It has Maclaurin series
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(6)
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(7)
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sine
