A334383 Decimal expansion of Sum_{k>=0} (-1)^k/(2^k*(k!)^2).

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

Offset: 0

Author

Ilya Gutkovskiy, Apr 25 2020

Keywords

• nonn
• cons

Examples

			1/(2^0*0!^2) - 1/(2^1*1!^2) + 1/(2^2*2!^2) - 1/(2^3*3!^2) + ... = 0.5591341444189799174882684679...
		

Links

• Index entries for sequences related to Bessel functions or polynomials
• Index entries for transcendental numbers

Crossrefs

Cf. A055546, A092605.

Bessel function values: A334380 (J(0,1)), this sequence (J(0,sqrt(2))), A091681 (J(0,2)), A197036 (I(0,1)), A334381 (I(0,sqrt(2))), A070910 (I(0,2)).

Programs

Mathematica

RealDigits[BesselJ[0, Sqrt[2]], 10, 110] [[1]]

PARI

besselj(0, sqrt(2)) \\ Michel Marcus, Apr 26 2020

Formula

Equals BesselJ(0,sqrt(2)).

Equals BesselI(0,sqrt(2)*i), where BesselI is the modified Bessel function of order 0. - Jianing Song, Sep 18 2021