

A085984


Decimal expansion of solution to e^x*(1 + x) == (1 + x)/e^x.


7



1, 1, 9, 9, 6, 7, 8, 6, 4, 0, 2, 5, 7, 7, 3, 3, 8, 3, 3, 9, 1, 6, 3, 6, 9, 8, 4, 8, 6, 4, 1, 1, 4, 1, 9, 4, 4, 2, 6, 1, 4, 5, 8, 7, 8, 8, 4, 1, 8, 6, 0, 7, 2, 0, 8, 9, 1, 5, 4, 7, 7, 7, 8, 3, 9, 1, 8, 1, 2, 4, 7, 2, 5, 2, 2, 3, 8, 4, 7, 4, 7, 9, 9, 9, 9, 0, 8, 6, 9, 9, 2, 1, 4, 6, 5, 0, 9, 3, 7, 9, 8, 8
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OFFSET

1,3


COMMENTS

This constant can also be defined as the root of coth x = x, as this equation and the above are equivalent.  Carl R. White, Dec 09 2003
This constant is also the point on the parametric tractrix (t  tanh t, sech t) the least distant from the origin.  Michael Clausen, Feb 18 2013
This constant also equals sqrt(lambda^2+1), where lambda is the Laplace limit constant A033259.  JeanFrançois Alcover, Sep 08 2014, after Steven Finch.


REFERENCES

Steven R. Finch, Mathematical constants, Volume 94, Encyclopedia of mathematics and its applications, Cambridge University Press, 2003, p. 268.


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000
Jogundas Armaitis, Molecules and Polarons in Extremely Imbalanced Fermi Mixtures, Master Thesis, Aug 11 2011, Institute for Theoretical Physics, Utrecht University.
Eric Weisstein's World of Mathematics, Kepler's Equation
Eric Weisstein's World of Mathematics, Laplace Limit
Eric Weisstein's World of Mathematics, Hyperbolic Cotangent


EXAMPLE

1.1996786402577338339163698486411419442614587884186072...


MATHEMATICA

RealDigits[ x /. FindRoot[ Coth[x] == x, {x, 1}, WorkingPrecision > 102]] // First (* JeanFrançois Alcover, Feb 08 2013 *)


PROG

(PARI) solve(u=1, 2, tanh(u)1/u) /* type e.g. \p99 to get 99 digits; M. F. Hasler, Feb 01 2011 */


CROSSREFS

Cf. A003957 (x = cos x), A009379, A033259.
Sequence in context: A157293 A146487 A195790 * A157245 A072908 A217695
Adjacent sequences: A085981 A085982 A085983 * A085985 A085986 A085987


KEYWORD

nonn,cons


AUTHOR

Eric W. Weisstein, Jul 06 2003


STATUS

approved



