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A016632 Decimal expansion of log(9). 5
2, 1, 9, 7, 2, 2, 4, 5, 7, 7, 3, 3, 6, 2, 1, 9, 3, 8, 2, 7, 9, 0, 4, 9, 0, 4, 7, 3, 8, 4, 5, 0, 5, 1, 4, 0, 9, 2, 9, 4, 9, 8, 1, 1, 1, 5, 6, 4, 5, 4, 9, 8, 9, 0, 3, 4, 6, 9, 3, 8, 8, 6, 6, 7, 2, 7, 4, 9, 8, 8, 5, 8, 6, 4, 3, 7, 2, 1, 7, 9, 3, 3, 7, 4, 7, 2, 3, 1, 5, 0, 9, 6, 2, 7, 4, 6, 4, 1, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
REFERENCES
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 2.
LINKS
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
FORMULA
log(9) = 2*Sum_{n >= 1} 1/(n*P(n, 5/4)*P(n-1, 5/4)), where P(n, x) denotes the n-th Legendre polynomial. The first 20 terms of the series gives the approximation log(9) = 2.19722457733(34...), correct to 11 decimal places. - Peter Bala, Mar 18 2024
EXAMPLE
2.197224577336219382790490473845051409294981115645498903469388667274988...
MATHEMATICA
First[RealDigits[Log[9], 10, 100]] (* Paolo Xausa, Mar 21 2024 *)
PROG
(PARI) default(realprecision, 20080); x=log(9); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b016632.txt", n, " ", d)); \\ Harry J. Smith, May 16 2009
CROSSREFS
Cf. A016737 Continued fraction.
Sequence in context: A086572 A349035 A316606 * A176400 A021459 A133169
KEYWORD
nonn,cons,changed
AUTHOR
STATUS
approved

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)