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A261069 Decimal expansion of J_5 = Integral_{0..Pi/2} x^5/sin(x) dx. 2
2, 6, 3, 4, 3, 1, 8, 2, 9, 0, 5, 1, 8, 7, 5, 5, 1, 6, 2, 2, 1, 0, 3, 1, 5, 9, 6, 1, 2, 8, 4, 0, 5, 5, 0, 5, 5, 9, 4, 0, 9, 3, 4, 3, 5, 8, 9, 3, 1, 5, 5, 5, 8, 4, 2, 1, 2, 3, 2, 1, 2, 3, 6, 9, 5, 8, 7, 1, 8, 0, 4, 6, 4, 0, 9, 5, 7, 1, 9, 1, 2, 7, 0, 2, 5, 2, 4, 0, 7, 0, 9, 7, 8, 2, 6, 6, 0, 5, 6, 2, 9, 8, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

J. M. Borwein, I. J. Zucker and J. Boersma, The evaluation of character Euler double sums, The Ramanujan Journal, April 2008, Volume 15, Issue 3, pp 377-405, see p. 13.

FORMULA

J_5 = (5*Catalan*Pi^4)/8 - (29*i*Pi^6)/2016 - 30*i*Pi^2*PolyLog(4, -i) + 240*i*PolyLog(6, -i).

Also equals (40*Pi^2*(32*Catalan*Pi^2 - PolyGamma(3, 1/4) + PolyGamma(3, 3/4)) + PolyGamma(5, 1/4) - PolyGamma(5, 3/4))/2048.

EXAMPLE

2.634318290518755162210315961284055055940934358931555842123212369587...

MATHEMATICA

J5 = (5*Catalan*Pi^4)/8 - (29*I*Pi^6)/2016 - 30*I*Pi^2*PolyLog[4, -I] +

     240*I*PolyLog[6, -I]; RealDigits[J5 // Re, 10, 103] // First

CROSSREFS

Cf. A006752 (J_1 / 2 = Catalan’s constant), A245073 (J_2), A225125 (J_3), A261068 (J_4).

Sequence in context: A066098 A299160 A123733 * A236557 A262943 A163892

Adjacent sequences:  A261066 A261067 A261068 * A261070 A261071 A261072

KEYWORD

nonn,cons

AUTHOR

Jean-François Alcover, Aug 08 2015

STATUS

approved

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Last modified March 31 02:36 EDT 2020. Contains 333135 sequences. (Running on oeis4.)