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Decimal expansion of Sum_{k>=0} 1/(2^k*(k!)^2).
8

%I #18 Sep 20 2021 10:49:45

%S 1,5,6,6,0,8,2,9,2,9,7,5,6,3,5,0,5,3,7,2,9,2,3,8,6,9,1,2,6,9,2,7,7,1,

%T 7,8,8,7,1,5,8,8,2,5,3,9,8,0,2,6,9,7,0,7,5,2,7,4,3,3,8,8,2,1,1,8,2,0,

%U 4,0,2,5,8,3,8,2,3,4,9,8,5,0,9,0,8,5,8,8,9,3,8,8,3,3,8,7,0,9,9,2,4,0,9,3,1,9,7,8,3,8

%N Decimal expansion of Sum_{k>=0} 1/(2^k*(k!)^2).

%H <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>

%F Equals BesselI(0,sqrt(2)).

%F Equals BesselJ(0,sqrt(2)*i). - _Jianing Song_, Sep 18 2021

%e 1/(2^0*0!^2) + 1/(2^1*1!^2) + 1/(2^2*2!^2) + 1/(2^3*3!^2) + ... = 1.56608292975635053729238691...

%t RealDigits[BesselI[0, Sqrt[2]], 10, 110] [[1]]

%o (PARI) suminf(k=0, 1/(2^k*(k!)^2)) \\ _Michel Marcus_, Apr 26 2020

%o (PARI) besseli(0, sqrt(2)) \\ _Michel Marcus_, Apr 26 2020

%Y Cf. A019774, A055546.

%Y Bessel function values: A334380 (J(0,1)), A334383 (J(0,sqrt(2)), A091681 (J(0,2)), A197036 (I(0,1)), this sequence (I(0,sqrt(2)), A070910 (I(0,2)).

%K nonn,cons

%O 1,2

%A _Ilya Gutkovskiy_, Apr 25 2020