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A254979 Decimal expansion of the mean Euclidean distance from a point in a unit 4D cube to the faces (named B_4(1) in Bailey's paper). 3
1, 1, 2, 1, 8, 9, 9, 6, 1, 8, 7, 1, 5, 8, 6, 0, 9, 7, 7, 3, 5, 1, 6, 1, 5, 1, 7, 5, 5, 6, 7, 5, 4, 2, 7, 0, 9, 2, 0, 0, 8, 0, 7, 9, 5, 6, 4, 3, 9, 5, 4, 5, 8, 3, 0, 8, 3, 6, 7, 9, 2, 4, 6, 6, 9, 1, 6, 4, 0, 3, 5, 4, 8, 6, 0, 6, 9, 1, 5, 3, 4, 9, 0, 2, 4, 6, 7, 3, 1, 4, 5, 5, 7, 8, 6, 3, 7, 6, 4, 4, 9, 7, 6, 3, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

D. H. Bailey, J. M. Borwein and R. E. Crandall, Box Integrals, J. Comp. Appl. Math. vol 206, no 1 (2007) 196.

D. H. Bailey, J. M. Borwein, and R. E. Crandall, Advances in the theory of box integrals, Math. Comp. 79 (271) (2010) 1839-1866, Table 2.

Eric Weisstein's World of Mathematics, Inverse Tangent Integral

Eric Weisstein's World of Mathematics, Polylogarithm

Eric Weisstein's World of Mathematics, Box Integral.

FORMULA

B_4(1) = 2/5 - Catalan/10 + (3/10)*Ti_2(3-2*sqrt(2)) + log(3) - (7*sqrt(2)/10) * arctan(1/sqrt(8)), where Ti_2(x) = (i/2)*(polylog(2, -i*x) - polylog(2, i*x)) (Ti_2 is the inverse tangent integral function).

EXAMPLE

1.12189961871586097735161517556754270920080795643954583...

MATHEMATICA

Ti2[x_] := (I/2)*(PolyLog[2, -I*x] - PolyLog[2, I*x]); B4[1] = 2/5 - Catalan/10 + (3/10)*Ti2[3 - 2*Sqrt[2]] + Log[3] - (7*Sqrt[2]/10)*ArcTan[1/Sqrt[8]] // Re; RealDigits[B4[1], 10, 105] // First

N[Integrate[1/u^2 - Pi^2*Erf[u]^4/(16*u^6), {u, 0, Infinity}]/Sqrt[Pi], 50] (* Vaclav Kotesovec, Aug 13 2019 *)

PROG

(Python)

from mpmath import *

mp.dps=106

x=3 - 2*sqrt(2)

Ti2x=(j/2)*(polylog(2, -j*x) - polylog(2, j*x))

C = 2/5 - catalan/10 + (3/10)*Ti2x + log(3) - (7*sqrt(2)/10)*atan(1/sqrt(8))

print([int(n) for n in str(C.real).replace('.', '')]) # Indranil Ghosh, Jul 04 2017

CROSSREFS

Cf. A130590, A244920, A244921, A254968.

Cf. A117653, A117654.

Sequence in context: A246403 A258502 A011019 * A261157 A193728 A295582

Adjacent sequences:  A254976 A254977 A254978 * A254980 A254981 A254982

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Feb 11 2015

STATUS

approved

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Last modified June 20 12:34 EDT 2021. Contains 345164 sequences. (Running on oeis4.)