[go: up one dir, main page]

login
A052119
Decimal expansion of number with continued fraction expansion 0, 1, 2, 3, 4, 5, 6, ...
22
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
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.
Eric Weisstein's World of Mathematics, Continued Fraction Constants.
Eric Weisstein's World of Mathematics, Generalized Continued Fraction.
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
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