#serretintegral — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #serretintegral, aggregated by home.social.
-
#OEIS #BBP-formulas #CatalanConstant #SerretIntegral
What I learned today (about Bailey-Borwein-Plouffe formulas).
Consider the integral
C = Integral_{x=0..1} arctan(x)/(x*(1 + x)) dx
I noticed two nice things about this constant.
(1) There is a BBP formula to compute it:
BBP formula (1/16) P(2, 16, 8, (8, 8, 4, 0, -2, -2, -1, 0))
(2) C = Catalan's constant minus Serret's integral.
In OEIS speak: A367053 = A006752 - A102886.
All of this is certainly trivial. Yet I think that these three constants belong together and should be treated together.
In her master's thesis "VERIFYING AND DISCOVERING BBP-TYPE FORMULAS", Melissa Larson gives a nice introduction to BBP-type formulas and lots of examples, but I didn't find the formula and the relations above.
https://www.d.umn.edu/~jgreene/masters_reports/BBP%20Paper%20final.pdf