A347139 - OEIS

A347139

Continued fraction expansion of the elementary charge in natural units.

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

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OFFSET

0,2

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.

LINKS

Table of n, a(n) for n=0..8.

Ronald Kleiss, Pictures, Paths, Particles, Processes.

Wikipedia, Elementary charge

FORMULA

No formula for the constant is known.

EXAMPLE

Decimal expansion: 0.30282212...

MATHEMATICA

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

CROSSREFS