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A016629
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Decimal expansion of log(6).
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12
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1, 7, 9, 1, 7, 5, 9, 4, 6, 9, 2, 2, 8, 0, 5, 5, 0, 0, 0, 8, 1, 2, 4, 7, 7, 3, 5, 8, 3, 8, 0, 7, 0, 2, 2, 7, 2, 7, 2, 2, 9, 9, 0, 6, 9, 2, 1, 8, 3, 0, 0, 4, 7, 0, 5, 8, 5, 5, 3, 7, 4, 3, 4, 3, 1, 3, 0, 8, 8, 7, 9, 1, 5, 1, 8, 8, 3, 0, 3, 6, 8, 2, 4, 7, 9, 4, 7, 9, 0, 8, 1, 8, 1, 0, 1, 5, 0, 7, 7
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refs;
listen;
history;
text;
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OFFSET
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1,2
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REFERENCES
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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.
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LINKS
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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].
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FORMULA
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log(6) = 2*Sum_{n >= 1} 1/(n*P(n, 7/5)*P(n-1, 7/5)), where P(n, x) denotes the n-th Legendre polynomial. The first 20 terms of the series gives the approximation log(6) = 1.79175946922805(27...), correct to 14 decimal places. - Peter Bala, Mar 19 2024
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EXAMPLE
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1.791759469228055000812477358380702272722990692183004705855374343130887...
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MATHEMATICA
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First[RealDigits[Log[6], 10, 100]] (* Paolo Xausa, Mar 21 2024 *)
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PROG
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(PARI) default(realprecision, 20080); x=log(6); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b016629.txt", n, " ", d)); \\ Harry J. Smith, May 16 2009
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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