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Decimal expansion of Pi*sqrt(2)*sqrt(2 + sqrt(2))/8.
4

%I #27 Oct 01 2022 00:23:00

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

%T 9,7,4,9,7,9,6,2,1,5,8,8,1,9,5,8,1,6,1,1,9,6,2,2,5,4,9,6,4,6,6,6,8,6,

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

%N Decimal expansion of Pi*sqrt(2)*sqrt(2 + sqrt(2))/8.

%D Jean-François Pabion, Éléments d'Analyse Complexe, licence de Mathématiques, page 111, Ellipses, 1995.

%H Philippe Flajolet and Robert Sedgewick, <a href="http://algo.inria.fr/flajolet/Publications/AnaCombi/anacombi.html">Analytic Combinatorics</a>, Cambridge Univ. Press, 2009, pp. 235-236.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals Integral_{x=0..oo} 1/(1 + x^8) dx.

%F Equals Pi*csc(Pi/8)/8.

%F Equals 1/Product_{k>=1} (1 - 1/(8*k)^2). - _Amiram Eldar_, Mar 12 2022

%e 1.02617215297703088887146778087283197497962...

%t First[RealDigits[N[Pi*Sqrt[2]Sqrt[2+Sqrt[2]]/8,95]]]

%o (PARI) Pi*sqrt(4 + 2*sqrt(2))/8 \\ _Michel Marcus_, Mar 07 2022

%Y Cf. A000796, A121601.

%Y Integral_{x=0..oo} 1/(1+x^m) dx: A019669 (m=2), A248897 (m=3), A093954 (m=4), A352324 (m=5), A019670 (m=6), this sequence (m=8), A094888 (m=10).

%K nonn,cons

%O 1,3

%A _Stefano Spezia_, Mar 05 2022