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A345411
Decimal expansion of the ratio between the position of the peak of the wavelength distribution of black-body radiation and the wavelength corresponding to the position of the peak of this distribution in the frequency domain.
0
5, 6, 8, 2, 5, 2, 6, 6, 0, 5, 4, 9, 7, 4, 3, 1, 3, 1, 1, 0, 4, 6, 5, 9, 3, 3, 8, 0, 2, 1, 7, 0, 4, 2, 5, 8, 7, 1, 5, 1, 2, 3, 0, 9, 4, 4, 4, 1, 1, 9, 4, 6, 7, 5, 7, 6, 7, 8, 6, 9, 7, 6, 5, 6, 3, 7, 4, 9, 0, 5, 6, 2, 2, 3, 4, 3, 8, 2, 1, 2, 6, 0, 8, 3, 8, 9, 4
OFFSET
0,1
COMMENTS
Equivalently, equals lambda_peak * nu_peak / c, where lambda_peak are nu_peak are the wavelength and frequency at which the maximum of the Planck function in the wavelength and frequency domains occurs, respectively, and c is the speed of light.
REFERENCES
Sean M. Stewart and R. Barry Johnson, Blackbody Radiation: A History of Thermal Radiation Computational Aids and Numerical Methods, CRC Press, 2016, eq. (2.39), p. 46.
LINKS
T. Richard Carson, Steps to the Planck Function: A Centenary Reflection, arXiv preprint astro-ph/0011219, 2000. See p. 10.
Wikipedia, Planck's law.
FORMULA
Equals (3 + W(-3*exp(-3)))/(5 + W(-5*exp(-5))) = A194567/A094090, where W(x) is Lambert's W-function.
EXAMPLE
0.56825266054974313110465933802170425871512309444119...
MATHEMATICA
RealDigits[(3 + ProductLog[-3/E^3])/(5 + ProductLog[-5/E^5]), 10, 100][[1]]
CROSSREFS
Sequence in context: A351885 A021180 A337711 * A275480 A091659 A271571
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Jun 18 2021
STATUS
approved