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

0,1

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]]

Crossrefs

Cf. A094090, A194567.

Sequence in context: A351885 A021180 A337711 * A275480 A091659 A271571

Adjacent sequences: A345408 A345409 A345410 * A345412 A345413 A345414

Keyword

nonn,cons

Author

Amiram Eldar, Jun 18 2021

Status

approved