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A221208 Decimal expansion of the Borwein integral with 8 sinc functions. 2

%I #34 Jan 04 2023 11:49:02

%S 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,

%T 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,

%U 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

%N Decimal expansion of the Borwein integral with 8 sinc functions.

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

%H Alois P. Heinz, <a href="/A221208/b221208.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/BorweinIntegrals.html">Borwein Integrals</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Borwein_integral">Borwein integral</a>

%F Equals 467807924713440738696537864469/935615849440640907310521750000*Pi. - _Alois P. Heinz_, Feb 28 2020

%F Equals Pi/2*A068214(7)/A144616(8). - _Andrey Zabolotskiy_, Jan 04 2023

%e 1.57079632677179604650584089424649585475065931838753259598...

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

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

%K cons,nonn,easy

%O 1,2

%A _Jean-François Alcover_, Feb 21 2013

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Last modified March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)