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A102521 Decimal expansion of value of Ahmed's 2nd integral. 3
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 (list; constant; graph; refs; listen; history; text; internal format)
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: A144408 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

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Last modified October 23 04:06 EDT 2021. Contains 348211 sequences. (Running on oeis4.)