The original pi/spigot work was done by Rabinowitz & Wagon [1]. See also the very readable works by Jeremy Gibbons [2] [3].

[1] https://en.wikipedia.org/wiki/Spigot_algorithm

[2] https://www.cs.ox.ac.uk/people/jeremy.gibbons/publications/s...

[3] https://seminar-materials.iijlab.net/iijlab-seminar/iijlab-s...