cp's OEIS Frontend

A175477 Decimal expansion of the dimension in which the sphere of unit radius has unit volume.

%I A175477 #16 Nov 05 2022 22:07:53
%S A175477 1,2,7,6,4,0,5,2,9,3,5,0,3,2,6,8,1,2,7,1,2,6,3,2,8,0,9,5,0,7,6,8,5,7,
%T A175477 4,7,6,1,9,9,8,4,0,4,7,3,2,5,6,1,4,3,7,0,6,0,5,8,7,5,7,2,0,7,4,1,3,0,
%U A175477 0,9,6,0,2,7,2,5,6,1,9,6,2,2,0,8,2,7,1,0,6,4,7,8,3,6,4,9,0,5,4,6,6,9,5,4,8
%N A175477 Decimal expansion of the dimension in which the sphere of unit radius has unit volume.
%C A175477 The positive solution x to Pi^(x/2)/Gamma(x/2+1) = 1.
%C A175477 Then Pi^(x/2) = 1488.75641500529701...
%C A175477 From _Mohammed Yaseen_, Sep 25 2022: (Start)
%C A175477 0 is another solution. All other solutions are negative.
%C A175477 This is also the dimension d in which the sphere of unit radius has surface area d. (End)
%H A175477 Mohammed Yaseen, <a href="/A175477/b175477.txt">Table of n, a(n) for n = 2..10000</a>
%H A175477 Wikipedia, <a href="http://en.wikipedia.org/wiki/N-sphere">N-sphere</a>
%e A175477 12.764052935032681271263280950768574761998...
%t A175477 x /. FindRoot[ Pi^(x/2)/Gamma[x/2 + 1] == 1, {x, 12}, WorkingPrecision -> 105] // RealDigits[#, 10, 105] & // First (* _Jean-François Alcover_, Feb 12 2013 *)
%o A175477 (PARI) solve(x=9,13,Pi^(x/2)-gamma(x/2+1)) \\ _Charles R Greathouse IV_, Jan 30 2016
%Y A175477 Cf. A074455, A074457.
%K A175477 cons,easy,nonn
%O A175477 2,2
%A A175477 _R. J. Mathar_, May 25 2010