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Search: id:A094644
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| A094644 |
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Continued fraction for e^gamma. |
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+0
1
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| 1, 1, 3, 1, 1, 3, 5, 4, 1, 1, 2, 2, 1, 7, 9, 1, 16, 1, 1, 1, 2, 6, 1, 2, 1, 6, 2, 59, 1, 1, 1, 3, 3, 3, 2, 1, 3, 5, 100, 1, 58, 1, 2, 1, 94, 1, 1, 2, 2, 10, 1, 2, 7, 1, 3, 4, 5, 3, 10, 1, 21, 1, 11, 1, 4, 1, 2, 2, 1, 2, 2, 1, 8, 3, 2, 1, 1, 6, 1, 2, 2, 1, 38, 2, 1, 4, 1, 3, 1, 1, 5, 3, 1, 52, 1, 2, 2, 1, 1
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Increasing partial quotients are: 1,3,5,7,9,16,59,100,129,314,2294,1568705
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REFERENCES
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J. Havil, Gamma, Exploring Euler's Constant, Princeton University Press, Princeton and Oxford, 2003, page 97.
G. Boros and V. Moll, Irresistible Integrals: Symbolics, Analysis, and Experiments in the Evaluation of Integrals, Cambridge University Press, Cambridge, 2004, Chap. 10.
J. Sondow, Double integrals for Euler's constant and ln(4/Pi) and an analogue of Hadjicostas's formula, Amer. Math. Monthly 112 (2005) 61-65.
J. Sondow, Criteria for irrationality of Euler's constant, Proc. Amer. Math. Soc. 131 (2003) 3335-3344.
J. Sondow, An antisymmetric formula for Euler's constant, Math. Mag. 71 (1998) 219-220.
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LINKS
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J. Sondow, An infinite product for e^gamma via hypergeometric formulas for Euler's constant, gamma.
J. Sondow, A faster product for pi and a new integral for ln pi/2
J. Sondow, A hypergeometric approach, via linear forms involving logarithms, to irrationality criteria for Euler's constant
J. Sondow and W. Zudilin, Euler's constant, q-logarithms, and formulas of Ramanujan and Gosper
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MATHEMATICA
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ContinuedFraction[ Exp[ EulerGamma], 100]
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CROSSREFS
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Cf. A073004.
Gamma is the Euler-Mascheroni constant A001620.
Sequence in context: A093803 A016599 A079650 this_sequence A113046 A133825 A114588
Adjacent sequences: A094641 A094642 A094643 this_sequence A094645 A094646 A094647
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KEYWORD
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cofr,easy,nonn
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AUTHOR
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Jonathan Sondow (jsondow(AT)alumni.princeton.edu) and Robert G. Wilson v (rgwv(AT)rgwv.com), May 18 2004
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