A352771 Decimal expansion of the unique real solution to exp(x) = 1/x - 1.

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

Offset

0,1

References

István Mező, The Lambert W Function, Its Generalizations and Applications, CRC Press, 2022.

Links

Table of n, a(n) for n=0..104.

István Mező and Árpád Baricz, On the generalization of the Lambert W function with applications in theoretical physics, arXiv:1408.3999 [math.CA], 2014-2015.

István Mező and Árpád Baricz, On the generalization of the Lambert W function, Trans. Amer. Math. Soc., Vol. 369, No. 11 (2017), pp. 7917-7934.

Formula

Equals W_1(1), where W_1(x) is the 1-Lambert function.

Equals 1/2 + Sum_{n>=2} (Sum_{k=1..n-1} ((n+k-1)!/(n-1)!) * Stirling2(n-1,k)*(-1/2)^k)/(2^n*n!).

Both formulas are from Mező and Baricz (2017).

Example

0.40105813754154703565062537500645662909560698650459...

Mathematica

RealDigits[x /. FindRoot[Exp[x] == 1/x - 1, {x, 1}, WorkingPrecision -> 120]][[1]]

Prog

(PARI) solve(x=0.1, 1, exp(x) - 1/x + 1) \\ Michel Marcus, Apr 02 2022

Crossrefs

Cf. A030178, A048993.

Sequence in context: A333274 A147311 A147312 * A271423 A372762 A019974

Adjacent sequences: A352768 A352769 A352770 * A352772 A352773 A352774

Keyword

nonn,cons

Author

Amiram Eldar, Apr 02 2022

Status

approved