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%I #14 Feb 24 2024 11:07:19
%S 1,0,2,7,8,4,7,2,6,1,5,9,7,4,1,5,7,9,9,6,9,2,6,8,8,4,9,3,0,8,0,7,9,2,
%T 3,6,3,7,3,0,3,4,3,3,1,0,2,8,3,4,2,5,7,2,5,4,7,1,2,4,5,0,2,2,8,2,6,7,
%U 2,5,6,9,2,7,3,2,3,3,2,8,1,8,8,5,7,3,5,2,7,8,8,3,5,1,5,2,8,2,6,6,4,6,7,6,7,9,2,3,7,8
%N Decimal expansion of Sum_{k>=0} 1/((2*k+1)!)^2.
%H <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>
%F Equals (BesselI(0,2) - BesselJ(0,2))/2.
%e 1/1!^2 + 1/3!^2 + 1/5!^2 + 1/7!^2 + ... = 1.027847261597415799692...
%e Continued fraction: 1 + 1/(36 - 36/(401 - 400/(1765 - ... - P(n-1)/((P(n) + 1) - ... )))), where P(n) = (2*n*(2*n + 1))^2 for n >= 1. - _Peter Bala_, Feb 22 2024
%t RealDigits[(BesselI[0, 2] - BesselJ[0, 2])/2, 10, 110] [[1]]
%o (PARI) suminf(k=0, 1/((2*k+1)!)^2) \\ _Michel Marcus_, Apr 26 2020
%o (PARI) (besseli(0,2) - besselj(0,2))/2 \\ _Michel Marcus_, Apr 26 2020
%Y Cf. A009445, A049469, A070910, A073742, A091681, A197036, A334379.
%K nonn,cons
%O 1,3
%A _Ilya Gutkovskiy_, Apr 25 2020
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