A221208 Decimal expansion of the Borwein integral with 8 sinc functions.

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

Offset: 1

Author

Jean-François Alcover, Feb 21 2013

Keywords

• cons
• nonn
• easy

Comments

The difference from Pi/2 (A019669) is approximately 0.231006*10^(-10).

Examples

			1.57079632677179604650584089424649585475065931838753259598...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• Eric Weisstein's MathWorld, Borwein Integrals
• Wikipedia, Borwein integral

Crossrefs

Cf. A000796, A019669, A068214, A068215, A144616, A091473.

Programs

Mathematica

Integrate[Product[Sinc[x/(2*k+1)], {k, 0, 7}], {x, 0, Infinity}] // RealDigits[#, 10, 105]& // First

Formula

Equals 467807924713440738696537864469/935615849440640907310521750000*Pi. - Alois P. Heinz, Feb 28 2020

Equals Pi/2*A068214(7)/A144616(7). - Andrey Zabolotskiy, Jan 04 2023