A347139 Continued fraction expansion of the elementary charge in natural units.

0, 3, 3, 3, 4, 9, 3, 1, 2

Offset: 0

Author

Chase Roycroft, Aug 19 2021

Keywords

• nonn
• cofr
• more

Comments

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).

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).

Alpha and e are energy-dependent (as described by a beta function). The value given here corresponds to the zero-energy limit.

Examples

			Decimal expansion: 0.30282212...
		

Links

• Ronald Kleiss, Pictures, Paths, Particles, Processes.
• Wikipedia, Elementary charge

Crossrefs

Cf. A347418 (decimal expansion).

Related to the fine structure constant (cf. A082726, A003673) and its reciprocal (A005600).

Programs

Mathematica

ContinuedFraction[Sqrt[4*Pi*UnitConvert[Quantity["Fine Structure Constant"]]]]

Formula

No formula for the constant is known.