A352125 Decimal expansion of Pi*sqrt(2)*sqrt(2 + sqrt(2))/8.

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, 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, 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

Offset: 1

Author

Stefano Spezia, Mar 05 2022

Keywords

• nonn
• cons

Examples

			1.02617215297703088887146778087283197497962...
		

References

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

Links

• Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics, Cambridge Univ. Press, 2009, pp. 235-236.
• Index entries for transcendental numbers.

Crossrefs

Cf. A000796, A047522, A121601.

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).

Programs

Mathematica

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

PARI

Pi*sqrt(4 + 2*sqrt(2))/8 \\ Michel Marcus, Mar 07 2022

Formula

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

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

Equals 1/Product_{k>=1} (1 - 1/(8*k)^2). - Amiram Eldar, Mar 12 2022

Equals Product_{k>=2} (1 + (-1)^k/A047522(k)). - Amiram Eldar, Nov 22 2024