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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
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
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
Sequence in context: A158244 A226580 A182007 * A179294 A259679 A247876
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved