This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A347139 #28 Jun 27 2023 10:29:06 %S A347139 0,3,3,3,4,9,3,1,2 %N A347139 Continued fraction expansion of the elementary charge in natural units. %C A347139 Elementary charge e (A081823) in units of the rationalized Planck charge sqrt(epsilon * h-bar * c), where epsilon = vacuum permittivity (A081799), h-bar = reduced Planck constant (A254181), c = speed of light (A003678). %C A347139 Similarly, the fine-structure constant (A082726) is the square of the elementary charge in units of the non-rationalized Planck charge sqrt(h-bar * c / k_e) where k_e = 1/(4*Pi*epsilon) is the Coulomb constant. As a result, they are related by e = sqrt(4*Pi*alpha). %C A347139 Alpha and e are energy-dependent (as described by a beta function). The value given here corresponds to the zero-energy limit. %H A347139 Ronald Kleiss, <a href="https://indico.nikhef.nl/event/617/attachments/4042/4749/Lectures-Kleiss_P4.pdf">Pictures, Paths, Particles, Processes</a>. %H A347139 Wikipedia, <a href="https://en.wikipedia.org/wiki/Elementary_charge">Elementary charge</a> %F A347139 No formula for the constant is known. %e A347139 Decimal expansion: 0.30282212... %t A347139 ContinuedFraction[Sqrt[4*Pi*UnitConvert[Quantity["Fine Structure Constant"]]]] %Y A347139 Cf. A347418 (decimal expansion). %Y A347139 Related to the fine structure constant (cf. A082726, A003673) and its reciprocal (A005600). %K A347139 nonn,cofr,more %O A347139 0,2 %A A347139 _Chase Roycroft_, Aug 19 2021