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

%I A052119 #48 Feb 16 2025 08:32:41
%S A052119 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,
%T A052119 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,
%U A052119 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
%N A052119 Decimal expansion of number with continued fraction expansion 0, 1, 2, 3, 4, 5, 6, ...
%D A052119 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 6.2, p. 423.
%H A052119 G. C. Greubel, <a href="/A052119/b052119.txt">Table of n, a(n) for n = 0..5000</a>
%H A052119 F. Amoretti, <a href="http://www.numdam.org/item/?id=NAM_1855_1_14__40_1">Sur la fraction continue [0,1,2,3,4,...]</a>, Nouvelles annales de mathématiques, 1ère série, tome 14 (1855), pp. 40-44.
%H A052119 Simon Plouffe, <a href="http://www.plouffe.fr/simon/constants/niceconst.txt">10000 digits</a>.
%H A052119 Simon Plouffe, <a href="http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap69.html">Bessell(1,2)/Bessell(0,2)</a>.
%H A052119 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ContinuedFractionConstants.html">Continued Fraction Constants</a>.
%H A052119 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GeneralizedContinuedFraction.html">Generalized Continued Fraction</a>.
%H A052119 <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>.
%F A052119 BesselI(1, 2)/BesselI(0, 2) = A096789/A070910. - _Henry Bottomley_, Jul 13 2001
%F A052119 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
%e A052119 0.697774657964007982006790592551752599486658...
%p A052119 evalf(BesselI(1, 2)/BesselI(0, 2), 120);  # _Alois P. Heinz_, Jan 25 2022
%t A052119 RealDigits[ FromContinuedFraction[ Range[0, 44]], 10, 110][[1]]
%t A052119 (* Or *) RealDigits[ BesselI[1, 2] / BesselI[0, 2], 10, 110] [[1]]
%t A052119 (* 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 *)
%o A052119 (PARI) besseli(1,2)/besseli(0,2) \\ _Charles R Greathouse IV_, Feb 19 2014
%Y A052119 Equals 1/A060997.
%K A052119 cons,easy,nonn,nice
%O A052119 0,1
%A A052119 Robert Lozyniak (11(AT)onna.com), Jan 21 2000
%E A052119 More terms from _Vladeta Jovovic_, Mar 30 2000
%E A052119 Entry revised by _N. J. A. Sloane_, Aug 13 2006