A102521 Decimal expansion of value of Ahmed's 2nd integral.

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

Offset: 1

Author

Eric W. Weisstein, Jan 14 2005

Keywords

• nonn
• cons

Examples

			0.590489270886385075159298139571568463546513361355639...
		

References

• Jonathan Borwein, David Bailey and Roland Girgensohn, Experimentation in Mathematics: Computational Paths to Discovery, A K Peters, 2004, p. 20.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000
• Eric Weisstein's World of Mathematics, Ahmed's Integral

Crossrefs

Cf. A096615, A098459.

Programs

Mathematica

RealDigits[Pi/4 - Pi/Sqrt[2] + (3*ArcTan[Sqrt[2]])/Sqrt[2], 10, 50][[1]] (* G. C. Greubel, Jun 02 2017 *)

PARI

Pi/4 - Pi/sqrt(2) + (3*atan(sqrt(2)))/sqrt(2) \\ G. C. Greubel, Jun 02 2017

Formula

Equals Pi/4 - Pi/sqrt(2) + (3*arctan(sqrt(2)))/sqrt(2).

Equals Integral_{x=0..1} arctan(sqrt(x^2 + 1))/(x^2 + 1)^(3/2) dx (Borwein et al., 2004). - Amiram Eldar, Aug 17 2020