login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A094090 Decimal expansion of positive solution to 5*(1-exp(u)) + u*exp(u) = 0. 6
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

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

FORMULA

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

EXAMPLE

u=4.965114231744276...

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A194567, A256500, A256501.

Sequence in context: A338142 A245299 A201415 * A200632 A186723 A008959

Adjacent sequences:  A094087 A094088 A094089 * A094091 A094092 A094093

KEYWORD

cons,nonn

AUTHOR

Jeppe Stig Nielsen, May 01 2004

EXTENSIONS

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 13:24 EST 2021. Contains 349563 sequences. (Running on oeis4.)