A098459 - OEIS

A098459

Decimal expansion of G/2 + (1/8)*Pi*log(2), where G is Catalan's constant (often also denoted K).

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

(list; constant; graph; refs; listen; history; text; internal format)

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

Table of n, a(n) for n=0..99.

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

Cf. A006752, A102886, A096615, A102521.

Sequence in context: A239120 A369134 A021582 * A171535 A245082 A019648

Adjacent sequences: A098456 A098457 A098458 * A098460 A098461 A098462

KEYWORD

nonn,cons,easy

AUTHOR

Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 08 2004

STATUS

approved