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A188141 Decimal expansion of integral ((arctan(1/x))^3,x=0..infinity). 1
1, 9, 7, 5, 4, 1, 6, 9, 7, 7, 0, 9, 8, 9, 0, 2, 4, 0, 9, 4, 6, 1, 2, 9, 6, 6, 9, 1, 4, 9, 8, 0, 1, 5, 8, 2, 7, 7, 1, 6, 7, 4, 5, 2, 6, 8, 7, 4, 7, 1, 2, 5, 5, 7, 1, 7, 8, 8, 3, 8, 6, 0, 5, 3, 6, 1, 5, 5, 1, 2, 6, 3, 9, 0, 0, 3, 0, 0, 4, 6, 8, 3, 2, 9, 0, 0, 1, 5, 9, 1, 1, 1, 8, 9, 3, 8, 9, 9, 8, 3, 6, 6, 9, 3, 2, 1, 2, 2, 0, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The computation of this integral was mentioned as a challenge by Robert Israel on the newsgroup sci.math (Dec 22 2010), a closed form solution being given by Valeri Astanoff.

LINKS

Table of n, a(n) for n=1..110.

The Math Forum at Drexel - Valeri Astanoff Re: Nice Integral, Dec 22, 2010.

EXAMPLE

1.9754169..

MATHEMATICA

RealDigits[N[(3/8)*(Pi^2*Log[4] - 7*Zeta[3]) , 110]][[1]]

(* or as a numerical check : *)

RealDigits[NIntegrate[ArcTan[1/x]^3, {x, 0, Infinity}, WorkingPrecision -> 110]][[1]] (* Jean-François Alcover, Mar 23 2011 *)

RealDigits[ N[ Integrate[ ArcTan[1/x]^3, {x, 0, Infinity}], 110]][[1]] (* Jean-François Alcover, Oct 19 2012, since version 6.0 *)

CROSSREFS

Cf. A086054 (int(arctan(1/x)^2, x=0..infinity)).

Sequence in context: A096230 A114433 A222129 * A244667 A307235 A194554

Adjacent sequences:  A188138 A188139 A188140 * A188142 A188143 A188144

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Mar 23 2011

STATUS

approved

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Last modified December 8 18:37 EST 2019. Contains 329865 sequences. (Running on oeis4.)