A093754 Decimal expansion of -Catalan + (Pi*arcsinh(1))/2 + HypergeometricPFQ[{1/2, 1, 1}, {3/2, 3/2}, 1/9]/6.

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

Offset: 0

Author

Eric W. Weisstein, Apr 15 2004

Keywords

• nonn
• cons

Examples

			0.63951035187031100196269308542732367987599462518472...
		

Links

• Eric Weisstein's World of Mathematics, Radial Integrals.

Crossrefs

Cf. A000796, A006752, A091648, A093753.

Programs

Mathematica

RealDigits[-Catalan + (Pi*ArcSinh[1])/2 + HypergeometricPFQ[{1/2, 1, 1}, {3/2, 3/2}, 1/9]/6, 10, 100][[1]] (* Amiram Eldar, Apr 12 2022 *)

Formula

Equals Integral_{x=0..1, y=0..1} 1/(x^2 + y^2 + 1) dy dx.

Equals Integral_{x=0..1} arccot(sqrt(x^2+1))/sqrt(x^2+1) dx. - Amiram Eldar, Apr 12 2022

Extensions

Keyword:cons added by R. J. Mathar, Apr 01 2010