A345411 - OEIS

%I #5 Jun 18 2021 21:58:50

%S 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,

%T 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,

%U 0,5,6,2,2,3,4,3,8,2,1,2,6,0,8,3,8,9,4

%N 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.

%C 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.

%D 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.

%H T. Richard Carson, <a href="https://arxiv.org/abs/astro-ph/0011219">Steps to the Planck Function: A Centenary Reflection</a>, arXiv preprint astro-ph/0011219, 2000. See p. 10.

%H Gerhard Kramm and Nicole Mölders, <a href="https://arxiv.org/abs/0901.1863">Planck's blackbody radiation law: Presentation in different domains and determination of the related dimensional constants</a>, arXiv:0901.1863 [physics.hist-ph], 2009.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Black-body_radiation">Black-body radiation</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Planck%27s_law">Planck's law</a>.

%F Equals (3 + W(-3*exp(-3)))/(5 + W(-5*exp(-5))) = A194567/A094090, where W(x) is Lambert's W-function.

%e 0.56825266054974313110465933802170425871512309444119...

%t RealDigits[(3 + ProductLog[-3/E^3])/(5 + ProductLog[-5/E^5]), 10, 100][[1]]

%Y Cf. A094090, A194567.

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Jun 18 2021