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A247319
Decimal expansion of integral_{0..Pi} x*log(2*cos(x/2))^2 dx, the first of two definite integrals studied by Rutledge and Douglas, and using the constant A_4 (A214508).
1
6, 4, 5, 3, 6, 5, 8, 4, 6, 3, 3, 4, 3, 4, 1, 0, 8, 1, 8, 9, 6, 2, 3, 3, 6, 0, 5, 1, 3, 1, 9, 1, 2, 9, 5, 3, 6, 0, 6, 5, 3, 0, 4, 1, 1, 6, 3, 6, 5, 2, 6, 0, 0, 7, 4, 6, 3, 4, 0, 6, 2, 3, 2, 2, 1, 0, 0, 7, 9, 4, 6, 5, 8, 8, 8, 4, 9, 6, 7, 1, 6, 9, 8, 2, 8, 7, 5, 7, 3, 3, 3, 5, 4, 8, 7, 0, 5, 7, 4, 9, 9, 8, 4, 7
OFFSET
1,1
LINKS
G. E. Raynor, On Serret's integral formula, Bull. Amer. Math. Soc. Volume 45, Number 12, Part 1 (1939), 911-917
G. Rutledge, R. D. Douglass, Table of definite integrals, Am. Math. Monthly 45 (1938) 525
FORMULA
A_4 + 31*Pi^4/480, where A_4 is A214508.
EXAMPLE
6.453658463343410818962336051319129536065304116365260074634...
MATHEMATICA
A4 = (13*Pi^4)/288 + (1/6)*Pi^2*Log[2]^2 - Log[2]^4/6 - 4*PolyLog[4, 1/2] - (7/2)*Log[2]*Zeta[3]; RealDigits[A4 + 31*Pi^4/480, 10, 104] // First
CROSSREFS
Sequence in context: A249185 A021159 A106332 * A342359 A140246 A130786
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved