A261068 Decimal expansion of J_4 = Integral_{0..Pi/2} x^4/sin(x) dx.

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

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, Volume 15, Issue 3 (April 2008), pp. 377-405; alternative link. See p. 13.

Formula

J_4 = Catalan*Pi^3 - 7*i*Pi^5/480 - 24*i*Pi*PolyLog(4, -i) + (93*zeta(5))/2.

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

Prog

(PARI) real(Catalan*Pi^3 - 7*I*Pi^5/480 - 24*I*Pi*polylog(4, -I) + 93*zeta(5)/2) \\ Amiram Eldar, Jun 27 2026

Crossrefs

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

Sequence in context: A360559 A254708 A132816 * A077453 A216982 A184854

Adjacent sequences: A261065 A261066 A261067 * A261069 A261070 A261071

Keyword

cons,nonn,changed

Author

Jean-François Alcover, Aug 08 2015

Status

approved