A086467 Decimal expansion of 2*arccsch(2)^2.
4, 6, 3, 1, 2, 9, 6, 4, 1, 1, 5, 4, 3, 8, 8, 7, 8, 4, 9, 9, 3, 8, 5, 8, 1, 4, 2, 4, 6, 3, 0, 6, 5, 5, 2, 0, 0, 3, 2, 8, 1, 2, 7, 0, 0, 0, 9, 8, 5, 9, 7, 7, 4, 1, 6, 3, 0, 6, 0, 2, 4, 5, 7, 3, 7, 9, 5, 9, 0, 6, 9, 1, 1, 3, 3, 9, 2, 3, 6, 2, 5, 9, 7, 0, 1, 0, 9, 0, 9, 4, 1, 7, 2, 7, 7, 6, 7, 9, 0, 1, 1, 1
Offset: 0
Examples
0.4631296...
Links
- Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 77.
- Renzo Sprugnoli, Sums of reciprocals of the central binomial coefficients, INTEGERS 6 (2006) #A27
- Eric Weisstein's World of Mathematics, Central Binomial Coefficient
- Index entries for transcendental numbers
Programs
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Mathematica
RealDigits[2ArcCsch[2]^2,10,120][[1]] (* Harvey P. Dale, Mar 07 2012 *)
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PARI
suminf(n=1, (-1)^(n-1)/n^2/binomial(2*n,n)) \\ Michel Marcus, Jul 31 2015
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PARI
2*asinh(.5)^2 \\ Charles R Greathouse IV, Nov 21 2024
Formula
Equals Sum_{n>=1} (-1)^(n-1)/n^2/binomial(2*n,n).
Equals Integral_{x=0..1} log(1+x-x^2)/x dx. - Vaclav Kotesovec, Jun 13 2021
Equals 2*A002390^2. - R. J. Mathar, Jun 07 2024