login
Decimal expansion of BesselI(1,2).
26

%I #32 Mar 21 2024 07:15:09

%S 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,

%T 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,

%U 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

%N Decimal expansion of BesselI(1,2).

%H A.H.M. Smeets, <a href="/A096789/b096789.txt">Table of n, a(n) for n = 1..20000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ModifiedBesselFunctionoftheFirstKind.html">Modified Bessel Function of the First Kind</a>.

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

%F 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

%F From _Amiram Eldar_, Jul 09 2023: (Start)

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

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

%e 1.59063685463732906338225...

%p evalf(BesselI(1,2)). # _R. J. Mathar_, Oct 16 2015

%t RealDigits[BesselI[1, 2], 10, 110][[1]]

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

%o (PARI) besseli(1,2) \\ _Charles R Greathouse IV_, Feb 19 2014

%Y Cf. A000108, A070910, A228229, A348607.

%K cons,easy,nonn

%O 1,2

%A _Robert G. Wilson v_, Jul 09 2004