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

Offset: 0

Author

Amiram Eldar, Jun 18 2021

Keywords

• nonn
• cons

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.

Examples

			0.56825266054974313110465933802170425871512309444119...
		

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.
• 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.

Crossrefs

Cf. A094090, A194567.

Programs

Mathematica

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

Formula

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