A265729 - OEIS

%I #15 Jul 05 2023 02:59:50

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

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

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

%N Decimal expansion of 32*Pi.

%C "The integral corresponds to integration over a spherical cone with opening angle pi/2 and radius 4. However, it is not clear what the integrand physically represents (it resembles computation of a moment of inertia, but that would give a factor (rho sin(phi))^2 rather than the given rho cos(phi)."

%D The Jun 02 1996 comic strip FoxTrot by Bill Amend (Amend 1998, p. 19; Mitchell 2006/2007)

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DefiniteIntegral.html">Definite Integral</a>

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

%F The triple Integral {0-2Pi}, {0-Pi/4}, {0-4} (rho*cos(phi)) rho^2 sin(phi) d(rho) d(phi) d(theta).

%e 100.53096491487338363080458826494409229430942078000338627119822695385012500...

%t RealDigits[32 Pi, 10, 111][[1]] (* or *)

%t Integrate[\[Rho] Cos[\[Phi]] \[Rho]^2 Sin[\[Phi]], {\[Rho], 0, 4}, {\[Phi], 0, Pi/4}, {\[Theta], 0, 2 Pi}]

%o (PARI) 32*Pi \\ _Altug Alkan_, Dec 14 2015

%Y Cf. A000796, A019692, A122952, A019694, A019669, A228719, A228721, A228824, A229939, A061146.

%K cons,nonn

%O 3,4

%A _Eric W. Weisstein_ and _Robert G. Wilson v_, Dec 14 2015