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%I #14 Sep 05 2019 09:34:18
%S 1,5,5,4,6,8,2,2,7,5,4,8,2,1,0,0,0,8,9,8,7,0,2,3,2,0,8,0,7,8,2,8,0,4,
%T 0,0,2,0,6,0,4,4,7,3,0,6,2,6,5,6,6,1,3,7,9,0,9,8,9,2,0,2,0,4,3,3,2,8,
%U 7,7,9,4,1,5,2,9,3,2,8,0,5,3,6,5,1,1,3,9,7,6,3,8,2,3,1,8,7,4,8,9,3,6,3,0,5
%N Decimal expansion of 4^(1/Pi).
%C Gosper found that lim[n approaches infinity] Prod[i=n..2n] Pi/2 arctan i = 4^(1/Pi) ~ 1.554682275...
%D Gosper, R. W. math-fun(AT)cs.arizona.edu posting, Sept. 1996.
%D Gosper, R. W. "a product." math-fun(AT)cs.arizona.edu posting, Sept. 27, 1996.
%H R. W. Gosper, <a href="http://www.tweedledum.com/rwg/idents.htm">Some identities</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PiFormulas.html">Pi Formulas</a>.
%e 1.5546822754821000898702320807828040020604473062656613790989...
%t RealDigits[4^(1/Pi),10,120][[1]] (* _Harvey P. Dale_, Sep 05 2019 *)
%o (Macsyma) 'limit(funmake_no_simp(".",[%pi/2/atan(n),%pi/2/atan(n+1),"","",%pi/2/atan(2*n)]),n,inf)=4^(1/%pi)
%K cons,easy,nonn
%O 1,2
%A _Jonathan Vos Post_, Apr 21 2006
%E More terms from _Eric W. Weisstein_, May 01 2006
%E Edited by _N. J. A. Sloane_, Jul 01 2008 at the suggestion of _R. J. Mathar_
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