A133838 Decimal expansion of the value at which Planck's radiation function achieves its maximum.

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

Offset

0,1

Comments

Consider the density of the radiation function (in wavelength form) B(lambda) = 2*h*c^2/{lambda^5*[exp(h*c/(kB*lambda*T))-1]}, where h is Planck's constant, c the speed of light, kB the Boltzmann constant, T the absolute temperature, and lambda the wavelength. Searching the maximum, we set the first derivative dB/dlambda to zero, then substitute x=lambda*T/(h*c/kB). The equation becomes 5+(1/x-5)*exp(1/x)=0 and the solution x is this constant here. - R. J. Mathar, Jan 30 2014

Links

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

Eric Weisstein's World of Mathematics, Planck's Radiation Function

Wikipedia, Wien's displacement law

Example

0.20140523527264218061... = 1/4.96511..

Mathematica

RealDigits[ x /. FindRoot[5x - E^(1/x)*(5x - 1), {x, 1/5}, WorkingPrecision -> 105]][[1]] (* or *)
1/(ProductLog[-5*Exp[-5]]+5) // RealDigits[#, 10, 105]& // First (* Jean-François Alcover, Nov 09 2012, updated Feb 27 2014, after Eric W. Weisstein *)

Crossrefs

Cf. A133839, A133840.

Sequence in context: A273821 A363519 A108643 * A182138 A258123 A121583

Adjacent sequences: A133835 A133836 A133837 * A133839 A133840 A133841

Keyword

nonn,cons,changed

Author

Eric W. Weisstein, Sep 26 2007

Status

approved