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

0,1

Comments

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

References

I. S. Gradshteyn and I. M. Rhyzhik, Tables of Integrals, Series and Products, Eq. 0.246.4

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.

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

Example

0.223890779...

Maple

BesselJ(0, 2) ; evalf(%) ; # R. J. Mathar, Mar 24 2026

Mathematica

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

Prog

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

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)).

Sequence in context: A046652 A319860 A300354 * A076541 A227380 A159789

Adjacent sequences: A091678 A091679 A091680 * A091682 A091683 A091684

Keyword

nonn,cons

Author

Eric W. Weisstein, Jan 28 2004

Status

approved