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

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, 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, 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

Offset

1,2

Links

Table of n, a(n) for n=1..110.

Index entries for sequences related to Bessel functions or polynomials

Formula

Equals BesselI(0,sqrt(2)).

Equals BesselJ(0,sqrt(2)*i). - Jianing Song, Sep 18 2021

Example

1/(2^0*0!^2) + 1/(2^1*1!^2) + 1/(2^2*2!^2) + 1/(2^3*3!^2) + ... = 1.56608292975635053729238691...

Mathematica

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

Prog

(PARI) suminf(k=0, 1/(2^k*(k!)^2)) \\ Michel Marcus, Apr 26 2020
(PARI) besseli(0, sqrt(2)) \\ Michel Marcus, Apr 26 2020

Crossrefs

Cf. A019774, A055546.

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)).

Sequence in context: A029944 A362582 A197494 * A153415 A154010 A258750

Adjacent sequences: A334378 A334379 A334380 * A334382 A334383 A334384

Keyword

nonn,cons

Author

Ilya Gutkovskiy, Apr 25 2020

Status

approved