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

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, 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, 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

Offset: 0

Author

Jeremy Tan, May 22 2016

Keywords

• nonn
• cons

Comments

This constant is multiplied into the CORDIC algorithm to obtain the correct sine or cosine. See p. 647 of the fxtbook (below).

Examples

			0.60725293500888125616944675250492826311239085215008977245...
		

Links

• Jeremy Tan, Table of n, a(n) for n = 0..249
• Joerg Arndt, Matters Computational (The Fxtbook), section 33.2
• Wikipedia, CORDIC

Crossrefs

Cf. A065445.

Programs

PARI

pent(z, n)= 1+sum(k=1, n, (-1)^k*(z^(k*(3*k-1)/2) + z^(k*(3*k+1)/2)));
/* == prod(n>=1, 1-z^n) via pentagonal number theorem */
N=30; u=0.25; K1=1/sqrt( 2 * pent(u^2, N)/pent(u, N) )
/* using prod(n>=1, 1+z^2) = prod(n>=1, 1-(z^2)^2)/prod(n>=1, 1-z^n) */
\\ Joerg Arndt, May 23 2016

Formula

Equals 1/A065445.