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%I #19 Sep 20 2021 10:50:33
%S 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 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 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 Decimal expansion of Sum_{k>=0} (-1)^k/((2*k)!!)^2.
%C This constant is transcendental.
%H <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Equals BesselJ(0,1).
%F Equals BesselI(0,i), where BesselI is the modified Bessel function of order 0. - _Jianing Song_, Sep 18 2021
%e 1/(4^0*0!^2) - 1/(4^1*1!^2) + 1/(4^2*2!^2) - 1/(4^3*3!^2) + ... = 0.765197686557966551449717526...
%t RealDigits[BesselJ[0, 1], 10, 110] [[1]]
%o (PARI) besselj(0, 1) \\ _Michel Marcus_, Apr 26 2020
%Y Cf. A000165, A002454.
%Y 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 nonn,cons
%O 0,1
%A _Ilya Gutkovskiy_, Apr 25 2020
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