A096615 Decimal expansion of 5 Pi^2/96.
5, 1, 4, 0, 4, 1, 8, 9, 5, 8, 9, 0, 0, 7, 0, 7, 6, 1, 3, 9, 7, 6, 2, 9, 7, 3, 9, 5, 7, 6, 8, 8, 2, 8, 7, 1, 6, 3, 0, 9, 2, 1, 8, 4, 4, 1, 2, 7, 1, 2, 4, 5, 1, 1, 7, 9, 2, 3, 6, 1, 9, 4, 6, 6, 7, 8, 1, 2, 7, 3, 3, 4, 5, 0, 1, 0, 0, 0, 2, 7, 3, 0, 7, 3, 0, 0, 9, 0, 3, 1, 4, 4, 3, 6, 7, 4, 5, 9, 5, 4, 0, 7
Offset: 0
Examples
0.514041895...
References
- Jonathan Borwein, David Bailey and Roland Girgensohn, Experimentation in Mathematics: Computational Paths to Discovery, A K Peters, Ltd., Natick, MA, 2004. x+357 pp. See pp. 17-20.
Links
- Zafar Ahmed, Problem 10884, The American Mathematical Monthly, Vol. 108, No. 6 (2001), p. 566, Definitely an Integral, solution to Problem 10884, solved by Knut Dale, George L. Lamb, the proposer and others, ibid., Vol. 109, No. 7 (2002), pp. 670-671.
- Zafar Ahmed, Ahmed's integral: the maiden solution, arXiv:1411.5169 [math.HO], 2014.
- Michael Penn, Ahmed's Integral, YouTube video, 2021.
- Juan Pla, A tale of Two Integrals: The Probability and Ahmed's Integrals, arXiv:1505.03314 [math.CA], 2015.
- Eric Weisstein's World of Mathematics, Ahmed's Integral
- Index entries for transcendental numbers
Programs
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Mathematica
RealDigits[5 Pi^2/96, 10 , 100][[1]] (* Amiram Eldar, Aug 17 2020 *)
Formula
From Amiram Eldar, Aug 17 2020: (Start)
Equals Integral_{x=0..1} arctan(sqrt(x^2 + 2))/(sqrt(x^2 + 2) * (x^2 + 1)) dx (Ahmed, 2001; Borwein et al., 2004).
Equals (1/10) * Integral_{x=1..oo} log(x)/(x^5 + x) dx. (End)