This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A334380 #24 Dec 21 2024 01:02:10
%S A334380 7,6,5,1,9,7,6,8,6,5,5,7,9,6,6,5,5,1,4,4,9,7,1,7,5,2,6,1,0,2,6,6,3,2,
%T A334380 2,0,9,0,9,2,7,4,2,8,9,7,5,5,3,2,5,2,4,1,8,6,1,5,4,7,5,4,9,1,1,9,2,7,
%U A334380 8,9,1,2,2,1,5,2,7,2,4,4,0,1,6,7,1,8,0,6,0,0,0,9,8,9,1,5,6,3,3,9,7,4,9,2,9,2,5,9,8,2
%N A334380 Decimal expansion of Sum_{k>=0} (-1)^k/((2*k)!!)^2.
%C A334380 This constant is transcendental.
%H A334380 <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>
%H A334380 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A334380 Equals BesselJ(0,1).
%F A334380 Equals BesselI(0,i), where BesselI is the modified Bessel function of order 0. - _Jianing Song_, Sep 18 2021
%e A334380 1/(4^0*0!^2) - 1/(4^1*1!^2) + 1/(4^2*2!^2) - 1/(4^3*3!^2) + ... = 0.765197686557966551449717526...
%t A334380 RealDigits[BesselJ[0, 1], 10, 110] [[1]]
%o A334380 (PARI) besselj(0, 1) \\ _Michel Marcus_, Apr 26 2020
%Y A334380 Cf. A000165, A002454.
%Y A334380 Bessel function values: this sequence (J(0,1)), A334383 (J(0,sqrt(2))), A091681 (J(0,2)), A197036 (I(0,1)), A334381 (I(0,sqrt(2))), A070910 (I(0,2)).
%K A334380 nonn,cons
%O A334380 0,1
%A A334380 _Ilya Gutkovskiy_, Apr 25 2020