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%I #12 Feb 24 2024 11:07:15
%S 1,2,5,1,7,3,8,0,4,0,7,3,8,6,5,1,4,6,7,7,4,4,5,1,5,9,4,7,7,3,0,7,4,0,
%T 9,8,9,5,5,5,4,9,7,7,9,2,5,0,2,0,3,3,3,2,8,5,9,9,5,9,4,7,2,8,8,3,7,5,
%U 7,9,6,5,0,5,0,0,3,4,3,5,2,3,8,7,2,1,6,4,3,0,0,2,0,4,9,5,7,6,3,2,5,1,6,9,1,6,2,8,2,7
%N Decimal expansion of Sum_{k>=0} 1/((2*k)!)^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.
%F Continued fraction: 1 + 1/(4 - 4/(145 - 144/(901 - ... - P(n-1)/((P(n) + 1) - ... )))), where P(n) = (2*n*(2*n - 1))^2. - _Peter Bala_, Feb 22 2024
%e 1/0!^2 + 1/2!^2 + 1/4!^2 + 1/6!^2 + ... = 1.25173804073865146774451594773...
%t RealDigits[(BesselI[0, 2] + BesselJ[0, 2])/2, 10, 110] [[1]]
%o (PARI) suminf(k=0, 1/((2*k)!)^2) \\ _Michel Marcus_, Apr 26 2020
%o (PARI) (besseli(0,2) + besselj(0,2))/2 \\ _Michel Marcus_, Apr 26 2020
%Y Cf. A010050, A049470, A070910, A073743, A091681, A197036, A334378.
%K nonn,cons
%O 1,2
%A _Ilya Gutkovskiy_, Apr 25 2020
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