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

1,1

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

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

Example

0.590489270886385075159298139571568463546513361355639...

Mathematica

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

Prog

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

Crossrefs

Cf. A096615, A098459.

Sequence in context: A371323 A019636 A269979 * A198615 A195372 A193017

Adjacent sequences: A102518 A102519 A102520 * A102522 A102523 A102524

Keyword

nonn,cons

Author

Eric W. Weisstein, Jan 14 2005

Status

approved