A244976 Decimal expansion of Pi/(8*sqrt(2)).

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

Offset: 0

Author

Jean-François Alcover, Jul 09 2014

Keywords

• nonn
• cons
• easy

Examples

			0.277680183634897890438492561878793356163413855585980638942837225434777...
		

References

• George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press (2006), Chapter 13 A Master Formula, p. 250.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Beta Function.
• Index entries for transcendental numbers

Crossrefs

Cf. A063448, A247719, A093954, A193887.

Programs

Mathematica

RealDigits[Pi/(8*Sqrt[2]), 10, 105] // First

PARI

Pi/(8*sqrt(2)) \\ G. C. Greubel, Jul 05 2017

Formula

Equals Integral_{x=0..1} (x^2*(1 + x^2))/(1 + x^4)^2 dx.

Equals beta(3/2, 1/2)/(4*sqrt(2)), where 'beta' is Euler's beta function.

Equals Sum_{k >= 0} (-1)^k * (2*k + 1)/((4*k + 1)*(4*k + 3)). - Peter Bala, Sep 21 2016

Equals Integral_{x>=0} 1/(x^2 + 2)^2 dx. - Amiram Eldar, Nov 16 2021