A334380 Decimal expansion of Sum_{k>=0} (-1)^k/((2*k)!!)^2.

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, 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, 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

Offset: 0

Author

Ilya Gutkovskiy, Apr 25 2020

Keywords

• nonn
• cons

Comments

This constant is transcendental.

Examples

			1/(4^0*0!^2) - 1/(4^1*1!^2) + 1/(4^2*2!^2) - 1/(4^3*3!^2) + ... = 0.765197686557966551449717526...
		

Links

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

Crossrefs

Cf. A000165, A002454.

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)).

Programs

Mathematica

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

PARI

besselj(0, 1) \\ Michel Marcus, Apr 26 2020

Formula

Equals BesselJ(0,1).

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