cp's OEIS Frontend

A334381 Decimal expansion of Sum_{k>=0} 1/(2^k*(k!)^2).

%I A334381 #23 Dec 21 2024 01:02:14
%S A334381 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 A334381 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 A334381 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 A334381 Decimal expansion of Sum_{k>=0} 1/(2^k*(k!)^2).
%H A334381 <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>
%F A334381 Equals BesselI(0,sqrt(2)).
%F A334381 Equals BesselJ(0,sqrt(2)*i). - _Jianing Song_, Sep 18 2021
%e A334381 1/(2^0*0!^2) + 1/(2^1*1!^2) + 1/(2^2*2!^2) + 1/(2^3*3!^2) + ... = 1.56608292975635053729238691...
%t A334381 RealDigits[BesselI[0, Sqrt[2]], 10, 110] [[1]]
%o A334381 (PARI) suminf(k=0, 1/(2^k*(k!)^2)) \\ _Michel Marcus_, Apr 26 2020
%o A334381 (PARI) besseli(0, sqrt(2)) \\ _Michel Marcus_, Apr 26 2020
%Y A334381 Cf. A019774, A055546.
%Y A334381 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 A334381 nonn,cons
%O A334381 1,2
%A A334381 _Ilya Gutkovskiy_, Apr 25 2020