A078434 - OEIS

%I #37 May 02 2024 07:06:45

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

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

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

%N Decimal expansion of zeta(3/2).

%H G. C. Greubel, <a href="/A078434/b078434.txt">Table of n, a(n) for n = 1..5000</a>

%H Alexander Sakhnovich and Lev Sakhnovich, <a href="https://doi.org/10.1007/978-3-319-10335-8_13">Nonlinear Fokker-Planck equation: stability, distance and the corresponding extremal problem in the spatially inhomogeneous case</a>, in: D. Alpay and B. Kirstein (eds.), Recent Advances in Inverse Scattering, Schur Analysis and Stochastic Processes, Birkhäuser, Cham, 2015, pp. 379-394; <a href="http://arxiv.org/abs/1307.1126">arXiv preprint</a>, arXiv:1307.1126 [math.AP], 2013-2015.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Bose-Einstein_condensate">Bose-Einstein condensate</a>.

%F Equals (2/sqrt(Pi))*Integral_{x>=0} sqrt(x)/(exp(x)-1) dx. - _Jean-François Alcover_, Nov 12 2013

%F Equals Gamma(-1/2)*zeta(-1/2)*tau(-1/2) where tau(s) = (2*Pi*i)^(-s) + (-2*Pi*i)^(-s). This follows from the functional equation of the Riemann zeta function. (Cf. A059750, A211113, A019707). - _Peter Luschny_, May 13 2020

%F Equals -4*Pi*zeta(-1/2) = 10 * A019694 * A211113. - _Amiram Eldar_, May 29 2021

%e 2.6123753486854883433485675679240716305708006524000634075733...

%t RealDigits[ Zeta[3/2], 10, 110][[1]]

%o (PARI) zeta(3/2) \\ _Charles R Greathouse IV_, Feb 06 2015

%Y Cf. A019694, A019707, A033461, A078470, A059750, A211113.

%K cons,nonn

%O 1,1

%A _Robert G. Wilson v_, Dec 30 2002