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%I #28 Feb 23 2024 02:14:55
%S 9,5,8,3,5,8,1,3,2,8,3,3,0,0,7,0,1,6,2,1,0,4,0,4,4,6,0,2,5,5,6,7,4,9,
%T 9,5,4,2,3,5,5,6,7,9,4,7,0,1,8,1,0,1,6,9,5,6,1,6,2,3,1,9,0,0,2,1,2,2,
%U 3,2,0,4,2,8,0,7,9,0,1,3,3,2,1,3,2,6,8
%N Decimal expansion of the constant Sum_{k>=0} (-1)^k/(4*k)!.
%H Michael I. Shamos, <a href="http://euro.ecom.cmu.edu/people/faculty/mshamos/cat.pdf">A catalog of the real numbers</a> (2011).
%F Equals cos(sqrt(2)/2)*cosh(sqrt(2)/2). - _Amiram Eldar_, Jul 18 2021
%F Continued fraction: 1/(1 + 1/(23 + 24/(1679 + ... + P(n-1)/((P(n) - 1) + ... )))), where P(n) = (4*n)*(4*n - 1)*(4*n - 2)*(4*n - 3) for n >= 1. Cf. A346441. - _Peter Bala_, Feb 21 2024
%e 0.95835813283300701621040446...
%t RealDigits[Sum[(-1)^k/(4*k)!, {k, 0, Infinity}], 10, 100][[1]] (* _Amiram Eldar_, Jul 18 2021 *)
%o (PARI) sumalt(k=0, (-1)^k/(4*k)!) \\ _Michel Marcus_, Jul 18 2021
%Y Cf. A068985, A049470, A346441, A346439, A346438, A346437, A346436, A346435, A196498.
%K cons,nonn
%O 0,1
%A _Sean A. Irvine_, Jul 17 2021
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