A096789 Decimal expansion of BesselI(1,2).

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

Offset: 1

Author

Robert G. Wilson v, Jul 09 2004

Keywords

• cons
• easy
• nonn

Examples

			1.59063685463732906338225...
		

Links

• A.H.M. Smeets, Table of n, a(n) for n = 1..20000
• I. S. Gradsteyn and I. M. Ryzhik, Table of integrals, series and products (6th ed.), 2000, (eq. 0.246.2).
• Eric Weisstein's World of Mathematics, Modified Bessel Function of the First Kind.

Crossrefs

Cf. A000108, A070910, A228229, A348607.

Programs

Maple

evalf(BesselI(1,2)). # R. J. Mathar, Oct 16 2015

Mathematica

RealDigits[BesselI[1, 2], 10, 110][[1]]
(* Or *) RealDigits[ Sum[ n/(n!n!), {n, 0, Infinity}], 10, 110][[1]]

PARI

besseli(1,2) \\ Charles R Greathouse IV, Feb 19 2014

Formula

Equals Sum_{k >= 0} k/k!^2.

Continued fraction expansion: 1/(1 - 1/(3 - 2/(7 - 6/(13 - 12/(21 - ... - n*(n-1)/(n^2+n+1 - ...)))))). For a sketch of the proof see A228229. Cf. A070910. - Peter Bala, Aug 19 2013

From Amiram Eldar, Jul 09 2023: (Start)

Equals exp(-2) * Sum_{k>=1} A000108(k)/(k-1)!.

Equals exp(2) * Sum_{k>=1} (-1)^(k+1) * A000108(k)/(k-1)!. (End)