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A070910 Decimal expansion of BesselI(0,2). 20
2, 2, 7, 9, 5, 8, 5, 3, 0, 2, 3, 3, 6, 0, 6, 7, 2, 6, 7, 4, 3, 7, 2, 0, 4, 4, 4, 0, 8, 1, 1, 5, 3, 3, 3, 5, 3, 2, 8, 5, 8, 4, 1, 1, 0, 2, 7, 8, 5, 4, 5, 9, 0, 5, 4, 0, 7, 0, 8, 3, 9, 7, 5, 1, 6, 6, 4, 3, 0, 5, 3, 4, 3, 2, 3, 2, 6, 7, 6, 3, 4, 2, 7, 2, 9, 5, 1, 7, 0, 8, 8, 5, 5, 6, 4, 8, 5, 8, 9, 8, 9, 8, 4, 5, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Factorial Sums

E. W. Weisstein, Modified Bessel Function of the First Kind

FORMULA

BesselI(0, 2) = sum_{k=0..inf} 1/k!^2 = 2.279585302336...

From Peter Bala, Aug 19 2013: (Start)

Continued fraction expansion: 1/(1 - 1/(2 - 1/(5 - 4/(10 - 9/(17 - ... - (n-1)^2/(n^2+1 - ...)))))). See A006040. Cf. A096789.

This continued fraction is the particular case k = 0 of the result BesselI(k,2) = sum {n = 0..inf} 1/(n!*(n+k)!) = 1/(k! - k!/((k+2) -(k+1)/((2*k+5) - 2*(k+2)/((3*k+10) - ... - n*(n+k)/(((n+1)*(n+k+1)+1) - ...))))). See the remarks in A099597 for a sketch of the proof. (End)

MATHEMATICA

RealDigits[ BesselI[0, 2], 10, 110] [[1]] (* Robert G. Wilson v, Jul 09 2004 *)

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

PROG

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

CROSSREFS

Cf. A096789, A070913 (continued fraction), A006040.

Sequence in context: A062305 A155063 A011022 * A189040 A267214 A107386

Adjacent sequences:  A070907 A070908 A070909 * A070911 A070912 A070913

KEYWORD

cons,easy,nonn

AUTHOR

Benoit Cloitre, May 20 2002

STATUS

approved

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Last modified July 25 18:14 EDT 2017. Contains 289796 sequences.