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A133838 Decimal expansion of the value at which Planck's radiation function achieves its maximum. 4
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 (list; constant; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Nov 09 2012, updated Feb 27 2014, after Eric W. Weisstein *)

CROSSREFS

Cf. A133839, A133840.

Sequence in context: A081265 A273821 A108643 * A182138 A258123 A121583

Adjacent sequences:  A133835 A133836 A133837 * A133839 A133840 A133841

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Sep 26 2007

STATUS

approved

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Last modified May 7 10:46 EDT 2021. Contains 343650 sequences. (Running on oeis4.)