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A058287
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Continued fraction for e^Pi.
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5
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23, 7, 9, 3, 1, 1, 591, 2, 9, 1, 2, 34, 1, 16, 1, 30, 1, 1, 4, 1, 2, 108, 2, 2, 1, 3, 1, 7, 1, 2, 2, 2, 1, 2, 3, 2, 166, 1, 2, 1, 4, 8, 10, 1, 1, 7, 1, 2, 3, 566, 1, 2, 3, 3, 1, 20, 1, 2, 19, 1, 3, 2, 1, 2, 13, 2, 2, 11, 3, 1, 2, 1, 7, 2, 1, 1, 1, 2, 1, 19, 1, 1, 12, 11, 1, 4, 1, 6, 1, 2, 18, 1, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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"The transcendentality of e^{Pi} was proved in 1929." (Wells)
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REFERENCES
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Jan Gullberg, "Mathematics, From the Birth of Numbers," W. W. Norton and Company, NY and London, 1997, page 86.
David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, Penguin Books, London, England, 1997, page 81.
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LINKS
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EXAMPLE
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e^Pi = 23.140692632779269005... = 23 + 1/(7 + 1/(9 + 1/(3 + 1/(1 + ...)))). - Harry J. Smith, Apr 19 2009
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MAPLE
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with(numtheory): cfrac(evalf((exp(1))^(evalf(Pi)), 2560), 256, 'quotients');
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MATHEMATICA
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ContinuedFraction[ E^Pi, 100]
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PROG
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(PARI) \p 300 contfrac(exp(1)^Pi)
(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(exp(1)^Pi); for (n=0, 20000, write("b058287.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Apr 19 2009
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CROSSREFS
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KEYWORD
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cofr,nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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