Arctangent function program [HP-42S, Free42]

[Gerson W. Barbosa]

(09-14-2024 01:43 PM)Thomas Klemm Wrote:  

(09-14-2024 10:42 AM)Gerson W. Barbosa Wrote:  which suggests that

atan(1/x) = 1/(x + 1^2/(3x + 2^2/(5x + 3^2/(7x + ... ))))

From Inverse Tangent:

Quote:The inverse tangent has continued fraction representations



(Lambert 1770; Lagrange 1776; Wall 1948, p. 343; Olds 1963, p. 138)

Yes, Thomas. That’s one of the many continued fraction representations for the arctangent(x) function l found when googling for them yesterday. What I have used is a continued fraction for arctangent(1/x). It appeared to me somewhat simpler to program, but I may be wrong. I would have to write programs for a few of those and see how they compare.

Cheers,

Gerson.