A094090 Decimal expansion of positive solution to 5*(1-exp(u)) + u*exp(u) = 0.

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

Offset: 1

Author

Jeppe Stig Nielsen, May 01 2004

Keywords

• cons
• nonn

Comments

This purely mathematical constant turns up when in physics one derives Wien's displacement law from the Planck black-body radiation law (see link).

Positive solution to x = 5*(1-exp(-x)). More comments in A256500. - Stanislav Sykora, Apr 01 2015

Examples

			u=4.965114231744276...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 1..2000
• NIST, Wien displacement law constant, in Fundamental Physical Constants.
• Eric Weisstein's World of Physics, Wien's Displacement Law
• Wikipedia, Planck's law
• Index entries for transcendental numbers

Crossrefs

Cf. A194567, A256500, A256501.

Programs

Mathematica

RealDigits[5 + ProductLog[ -5/E^5], 10, 120][[1]] (* Robert G. Wilson v, May 04 2004 *)

PARI

a5=solve(x=0.1, 10, x-5*(1-exp(-x))) \\ Use real precision in excess

Formula

u = 5 + W(-5*exp(-5)), where W() is Lambert's W-function.

Extensions

More terms from Robert G. Wilson v, May 04 2004