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A273413 Decimal expansion of Product_{k>=0} (1 + 1/2^(2k))^(-1/2).

%I A273413 #13 May 23 2016 08:39:19
%S A273413 6,0,7,2,5,2,9,3,5,0,0,8,8,8,1,2,5,6,1,6,9,4,4,6,7,5,2,5,0,4,9,2,8,2,
%T A273413 6,3,1,1,2,3,9,0,8,5,2,1,5,0,0,8,9,7,7,2,4,5,6,9,7,6,0,1,3,1,1,0,1,4,
%U A273413 7,8,8,1,2,0,8,4,2,4,9,0,6,9,0,6,2,2,7,4,2,5,9,0,8,0,3,8,4,0,5,2,7,4
%N A273413 Decimal expansion of Product_{k>=0} (1 + 1/2^(2k))^(-1/2).
%C A273413 This constant is multiplied into the CORDIC algorithm to obtain the correct sine or cosine. See p. 647 of the fxtbook (below).
%H A273413 Jeremy Tan, <a href="/A273413/b273413.txt">Table of n, a(n) for n = 0..249</a>
%H A273413 Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>, section 33.2
%H A273413 Wikipedia, <a href="https://en.wikipedia.org/wiki/CORDIC">CORDIC</a>
%F A273413 Equals 1/A065445.
%e A273413 0.60725293500888125616944675250492826311239085215008977245...
%o A273413 (PARI)
%o A273413 pent(z, n)= 1+sum(k=1, n, (-1)^k*(z^(k*(3*k-1)/2) + z^(k*(3*k+1)/2)));
%o A273413 /* == prod(n>=1, 1-z^n) via pentagonal number theorem */
%o A273413 N=30; u=0.25; K1=1/sqrt( 2 * pent(u^2, N)/pent(u, N) )
%o A273413 /* using prod(n>=1, 1+z^2) = prod(n>=1, 1-(z^2)^2)/prod(n>=1, 1-z^n) */
%o A273413 \\ _Joerg Arndt_, May 23 2016
%Y A273413 Cf. A065445.
%K A273413 nonn,cons
%O A273413 0,1
%A A273413 _Jeremy Tan_, May 22 2016