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A261068 Decimal expansion of J_4 = Integral_{0..Pi/2} x^4/sin(x) dx. 2
2, 0, 5, 3, 1, 6, 0, 7, 3, 1, 4, 8, 0, 5, 9, 1, 6, 6, 8, 9, 5, 6, 5, 4, 1, 2, 9, 6, 0, 2, 6, 5, 1, 1, 3, 6, 6, 8, 5, 6, 5, 5, 8, 8, 4, 4, 5, 7, 2, 3, 9, 5, 6, 9, 4, 3, 8, 5, 1, 8, 8, 9, 2, 7, 6, 5, 2, 2, 9, 2, 3, 4, 2, 3, 7, 9, 1, 9, 1, 7, 7, 1, 7, 6, 7, 7, 6, 9, 8, 0, 7, 8, 9, 0, 1, 7, 4, 2, 6, 7, 3, 2 (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_4 = Catalan*Pi^3 - 7*i*Pi^5/480 - 24*i*Pi*PolyLog(4, -i) + (93*zeta(5))/2.

Also equals Catalan*Pi^3 + (1/64)*(Pi*(PolyGamma(3, 3/4) - PolyGamma(3, 1/4)) + 2976*Zeta(5));

EXAMPLE

2.05316073148059166895654129602651136685655884457239569438518892765...

MATHEMATICA

J4 = Catalan*Pi^3 - 7*I*Pi^5/480 - 24*I*Pi*PolyLog[4, -I] + 93*Zeta[5]/2; RealDigits[J4 // Re, 10, 102] // First

CROSSREFS

Cf. A006752 (J_1 / 2 = Catalan’s constant), A245073 (J_2), A225125 (J_3), A261069 (J_5).

Sequence in context: A014842 A254708 A132816 * A077453 A216982 A184854

Adjacent sequences:  A261065 A261066 A261067 * A261069 A261070 A261071

KEYWORD

cons,nonn

AUTHOR

Jean-François Alcover, Aug 08 2015

STATUS

approved

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Last modified March 29 17:23 EDT 2020. Contains 333116 sequences. (Running on oeis4.)