A247320 Decimal expansion of integral_{0..Pi} log(x)/x*log(1 + x)^2 dx, the second of two definite integrals studied by Rutledge and Douglas.

1, 7, 5, 5, 7, 1, 3, 4, 3, 1, 3, 7, 3, 1, 0, 6, 0, 4, 0, 7, 3, 1, 8, 6, 5, 8, 9, 9, 9, 5, 5, 2, 3, 8, 6, 8, 4, 3, 0, 0, 4, 5, 4, 6, 4, 1, 3, 6, 9, 4, 2, 2, 3, 4, 9, 2, 4, 1, 6, 6, 9, 9, 7, 4, 9, 4, 4, 4, 4, 1, 1, 5, 2, 6, 0, 2, 1, 7, 0, 1, 5, 3, 3, 2, 3, 1, 4, 1, 8, 6, 5, 9, 4, 2, 0, 6, 2, 4, 3, 0, 6, 7, 3

Offset

1,2

Links

Table of n, a(n) for n=1..103.

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 - Pi^4/288, where A_4 is A214508.

Example

-0.175571343137310604073186589995523868430045464136942234924...

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 - Pi^4/288, 10, 103] // First

Crossrefs

Cf. A214508, A247319.

Sequence in context: A158244 A226580 A182007 * A179294 A259679 A247876

Adjacent sequences: A247317 A247318 A247319 * A247321 A247322 A247323

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Sep 12 2014

Status

approved