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

1,2

Links

A.H.M. Smeets, Table of n, a(n) for n = 1..20000

Eric Weisstein's World of Mathematics, Modified Bessel Function of the First Kind.

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)

Example

1.59063685463732906338225...

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]]

Prog

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

Crossrefs

Cf. A000108, A070910, A228229, A348607.

Sequence in context: A195372 A193017 A277651 * A342714 A261623 A298515

Adjacent sequences: A096786 A096787 A096788 * A096790 A096791 A096792

Keyword

cons,easy,nonn,changed

Author

Robert G. Wilson v, Jul 09 2004

Status

approved