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
Examples
0.697774657964007982006790592551752599486658...
References
- Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 6.2, p. 423.
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.
Crossrefs
Equals 1/A060997.
Programs
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Maple
evalf(BesselI(1, 2)/BesselI(0, 2), 120); # Alois P. Heinz, Jan 25 2022
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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 *) -
PARI
besseli(1,2)/besseli(0,2) \\ Charles R Greathouse IV, Feb 19 2014
Formula
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
Extensions
More terms from Vladeta Jovovic, Mar 30 2000
Entry revised by N. J. A. Sloane, Aug 13 2006