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A086054 Decimal expansion of Pi*log(2). 6
2, 1, 7, 7, 5, 8, 6, 0, 9, 0, 3, 0, 3, 6, 0, 2, 1, 3, 0, 5, 0, 0, 6, 8, 8, 8, 9, 8, 2, 3, 7, 6, 1, 3, 9, 4, 7, 3, 3, 8, 5, 8, 3, 7, 0, 0, 3, 6, 9, 2, 8, 6, 2, 9, 4, 3, 2, 5, 7, 9, 5, 2, 5, 3, 1, 9, 4, 3, 0, 8, 5, 4, 9, 1, 7, 6, 7, 4, 1, 9, 8, 6, 4, 3, 0, 3, 2, 8, 9, 6, 1, 6, 1, 0, 6, 6, 3, 0, 2, 5, 0, 5, 7, 6, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Madelung constant b2(2), negated.

LINKS

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Madelung Constants

FORMULA

Pi*log(2) = -(8/3)*int(log(x)/sqrt(1+4*x-4*x^2), x=0..1). - John M. Campbell, Feb 07 2012

Pi*log(2) = int((x/sin(x))^2, x=0..Pi/2) = int(log(x^2+1)/(x^2+1), x=0..infinity) = int(-log(cos(x)), x=-Pi/2..Pi/2) = int(arctan(1/x)^2, x=0..infinity). - Jean-Fran├žois Alcover, May 30 2013

From Amiram Eldar, Jul 11 2020: (Start)

Equals Integral_{x=-1..1} arcsin(x) dx / x.

Equals Integral_{x=-Pi/2..Pi/2} x*cot(x) dx. (End)

EXAMPLE

2.1775860903036021305006888982376139...

MATHEMATICA

RealDigits[Pi Log[2], 10, 120][[1]] (* Harvey P. Dale, Dec 31 2011 *)

CROSSREFS

Cf. A000796 (Pi), A002162 (log(2)).

Sequence in context: A072280 A217106 A329995 * A256392 A011134 A157240

Adjacent sequences:  A086051 A086052 A086053 * A086055 A086056 A086057

KEYWORD

nonn,cons,easy

AUTHOR

Eric W. Weisstein, Jul 07 2003

EXTENSIONS

Corrected by Antti Ahti (antti.ahti(AT)tkk.fi), Nov 17 2004

More terms from Benoit Cloitre, May 21 2005

STATUS

approved

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Last modified September 18 22:34 EDT 2021. Contains 347548 sequences. (Running on oeis4.)