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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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..104.

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

Cf. A214508, A247320.

Sequence in context: A249185 A021159 A106332 * A140246 A130786 A197295

Adjacent sequences:  A247316 A247317 A247318 * A247320 A247321 A247322

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Sep 12 2014

STATUS

approved

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Last modified August 22 00:43 EDT 2019. Contains 326169 sequences. (Running on oeis4.)