A345411 - OEIS

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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.

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

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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

Table of n, a(n) for n=0..86.

T. Richard Carson, Steps to the Planck Function: A Centenary Reflection, arXiv preprint astro-ph/0011219, 2000. See p. 10.

Gerhard Kramm and Nicole Mölders, Planck's blackbody radiation law: Presentation in different domains and determination of the related dimensional constants, arXiv:0901.1863 [physics.hist-ph], 2009.

Wikipedia, Black-body radiation.

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]]