[PROJ] Arc length of an ellipse

[Pierre Abbat]

I'd like to make a separate transmer program which will compute the Fourier 
series coefficients for transverse Mercator with greater precision than the 
transmer program in Bezitopo does. To do this, I need to compute the arc 
length from the equator to any point along the meridian of an ellipsoid. 
Wikipedia says that elliptic integrals came from computing the arc length of 
an ellipse, but doesn't explain how to compute the arc length using elliptic 
functions. Do you know how to do this?

I won't get around to doing this until late March at the earliest. I'm going 
to present at the MAA sectional, and to compute in 16-byte floats I need a 
Power9 box, which I don't have yet.

Pierre
-- 
The Black Garden on the Mountain is not on the Black Mountain.