A052119 Decimal expansion of number with continued fraction expansion 0, 1, 2, 3, 4, 5, 6, ...

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

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

F. Amoretti, Sur la fraction continue [0,1,2,3,4,...], Nouvelles annales de mathématiques, 1ère série, tome 14 (1855), pp. 40-44.

Simon Plouffe, 10000 digits.

Simon Plouffe, Bessell(1,2)/Bessell(0,2).

Eric Weisstein's World of Mathematics, Continued Fraction Constants.

Eric Weisstein's World of Mathematics, Generalized Continued Fraction.

Index entries for sequences related to Bessel functions or polynomials.

Formula

BesselI(1, 2)/BesselI(0, 2) = A096789/A070910. - Henry Bottomley, Jul 13 2001

Equivalently, the value of this continued fraction is the ratio of the sums: sum_{n=0..inf} n/(n!n!) and sum_{n=0..inf} 1/(n!n!). - Robert G. Wilson v, Jul 09 2004

Example

0.697774657964007982006790592551752599486658...

Maple

evalf(BesselI(1, 2)/BesselI(0, 2), 120);  # Alois P. Heinz, Jan 25 2022

Mathematica

RealDigits[ FromContinuedFraction[ Range[0, 44]], 10, 110][[1]]
(* Or *) RealDigits[ BesselI[1, 2] / BesselI[0, 2], 10, 110] [[1]]
(* Or *) RealDigits[ Sum[n/(n!n!), {n, 0, Infinity}] / Sum[1/(n!n!), {n, 0, Infinity}], 10, 110] [[1]] (* Robert G. Wilson v, Jul 09 2004 *)

Prog

(PARI) besseli(1, 2)/besseli(0, 2) \\ Charles R Greathouse IV, Feb 19 2014

Crossrefs

Equals 1/A060997.

Sequence in context: A019813 A096767 A247844 * A021593 A371134 A344083

Adjacent sequences: A052116 A052117 A052118 * A052120 A052121 A052122

Keyword

cons,easy,nonn,nice

Author

Robert Lozyniak (11(AT)onna.com), Jan 21 2000

Extensions

More terms from Vladeta Jovovic, Mar 30 2000

Entry revised by N. J. A. Sloane, Aug 13 2006

Status

approved