login
A098459
Decimal expansion of G/2 + (1/8)*Pi*log(2), where G is Catalan's constant (often also denoted K).
2
7, 3, 0, 1, 8, 1, 0, 5, 8, 3, 7, 6, 5, 5, 9, 7, 7, 3, 8, 3, 9, 8, 8, 7, 8, 6, 9, 7, 4, 5, 8, 9, 3, 7, 9, 8, 8, 0, 4, 3, 9, 7, 6, 4, 9, 6, 8, 6, 9, 9, 6, 8, 5, 3, 9, 2, 3, 9, 7, 3, 4, 6, 6, 4, 6, 0, 1, 7, 0, 0, 7, 8, 5, 3, 5, 2, 2, 0, 1, 3, 3, 0, 4, 3, 4, 6, 9, 3, 7, 6, 6, 6, 4, 3, 9, 0, 4, 3, 1, 2
OFFSET
0,1
REFERENCES
Jonathan Borwein, David Bailey and Roland Girgensohn, Experimentation in Mathematics: Computational Paths to Discovery, A K Peters, 2004, p. 20.
LINKS
Eric Weisstein's World of Mathematics, Ahmed's Integral
FORMULA
Equals Integral_{x=0..1} arctan(x) / (x*(x^2+1)) dx.
From Amiram Eldar, Aug 17 2020: (Start)
Equals (1/2) * A006752 + A102886.
Equals Integral_{x=0..Pi/4} x*cot(x) dx. (End)
EXAMPLE
0.7301810583765597738398878697...
MATHEMATICA
RealDigits[Catalan/2 + Pi*Log[2]/8, 10 , 100][[1]] (* Amiram Eldar, Aug 17 2020 *)
CROSSREFS
KEYWORD
nonn,cons,easy
AUTHOR
Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 08 2004
STATUS
approved