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A301484 Decimal expansion of J_0(2)/J_1(2) = 1 - 1/(2 - 1/(3 - 1/(4 - ...))). 0
3, 8, 8, 2, 1, 0, 7, 6, 5, 5, 6, 7, 7, 9, 5, 7, 8, 7, 5, 1, 1, 6, 5, 8, 5, 5, 7, 3, 0, 6, 5, 3, 7, 0, 2, 9, 2, 2, 1, 7, 4, 5, 0, 4, 0, 7, 2, 5, 3, 2, 9, 8, 1, 8, 6, 4, 6, 4, 2, 8, 2, 7, 5, 9, 3, 7, 3, 5, 1, 7, 3, 9, 5, 6, 3, 8, 2, 4, 2, 0, 1, 2, 1, 1, 0, 1, 9, 3, 5, 1, 6, 2, 8, 2, 8, 0, 3, 1, 9, 6, 0, 5, 2, 1, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

These are the first 105 decimal digits of the constant defined by the continued fraction 1 - 1/(2 - 1/(3 - 1/(4 - ... -1/m))) as m goes to infinity. The continued fraction appears to converge fairly rapidly. Just 50 terms, for instance, suffices to produce a numerical value that appears to be good to 100 digits, based on comparisons with more terms and higher precision. This sequence was brought to the author's attention by Beresford Parlett of U.C. Berkeley.

Addendum: This sequence has been identified by Karl Dilcher. He noted that the sequence of continued fraction convergents is the same as A058797. In short, the real constant whose decimal expansion is given above is given by BesselJ[0,2]/BesselJ[1,2] (Mathematica expression). The comments at A058797 have quite a bit of additional information and references.

LINKS

Table of n, a(n) for n=0..104.

FORMULA

Equals BesselJ(0,2)/BesselJ(1,2).

EXAMPLE

0.38821076556779578751165855730653702922174504072532981864642827593735174...

MATHEMATICA

1+ContinuedFractionK[(-1)^(n+1)*n, {n, 2, Infinity}]

N[1+ContinuedFractionK[(-1)^(n+1)*n, {n, 2, 50}], 105] (* 105 decimals *)

PROG

(PARI) default(realprecision, 100); besselj(0, 2)/besselj(1, 2) \\ Altug Alkan, Mar 22 2018

CROSSREFS

Cf. A058797, A091681, A296168.

Sequence in context: A019630 A101749 A206431 * A249451 A019744 A252876

Adjacent sequences:  A301481 A301482 A301483 * A301485 A301486 A301487

KEYWORD

nonn,cons

AUTHOR

David H Bailey, Mar 22 2018

STATUS

approved

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Last modified March 25 20:38 EDT 2019. Contains 321477 sequences. (Running on oeis4.)