A119858 Decimal expansion of area bounded by x->x and x->Log[x! ] on 0 <= x <= c, where c is the value given by A078335.

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

Offset: 1

Author

Joseph Biberstine (jrbibers(AT)indiana.edu), Jul 30 2006

Keywords

• cons
• nonn

Examples

			4.66201670318211134091107036412...
		

Crossrefs

Cf. Upper bound of integral is given by A078335.

Programs

Mathematica

RealDigits[NIntegrate[x - Log[x! ], {x, 0, FindRoot[r - Log[r! ], {r,5.29}, WorkingPrecision -> 200][[1]][[2]]}, WorkingPrecision -> 40]]

PARI

intnum(x=0, solve(x=5.2, 5.3, exp(x)-gamma(1+x)) , x - log(gamma(x+1))) \\ Michel Marcus, Apr 05 2015

Extensions

More terms from Robert G. Wilson v, Jan 07 2016