A091681 Decimal expansion of BesselJ(0,2).

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

Offset: 0

Author

Eric W. Weisstein, Jan 28 2004

Keywords

• nonn
• cons

Comments

The Pierce Expansion of this number is the squares > 1: 4,9,16,25,... - Franklin T. Adams-Watters, May 22 2006

Examples

			0.223890779...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2500
• Eric Weisstein's World of Mathematics, Factorial Sums
• Eric Weisstein's World of Mathematics, Pierce Expansion

Crossrefs

Cf A000290, A068985, A073701.

Bessel function values: A334380 (J(0,1)), A334383 (J(0,sqrt(2))), this sequence (J(0,2)), A197036 (I(0,1)), A334381 (I(0,sqrt(2))), A070910 (I(0,2)).

Programs

Mathematica

RealDigits[N[BesselJ[0, 2], 250]][[1]] (* G. C. Greubel, Dec 26 2016 *)

PARI

besselj(0,2) \\ Charles R Greathouse IV, Feb 19 2014

Formula

Equals Sum_{k>=0} (-1)^k/(k!)^2.

Continued fraction expansion: BesselJ(0,2) = 1/(4 + 4/(8 + 9/(15 + ... + (n - 1)^2/(n^2 + 1 + ...)))). See A073701 for a proof. - Peter Bala, Feb 01 2015

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