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A347139
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Continued fraction expansion of the elementary charge in natural units.
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1
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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FORMULA
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No formula for the constant is known.
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EXAMPLE
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Decimal expansion: 0.30282212...
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MATHEMATICA
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ContinuedFraction[Sqrt[4*Pi*UnitConvert[Quantity["Fine Structure Constant"]]]]
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CROSSREFS
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KEYWORD
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nonn,cofr,more
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AUTHOR
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STATUS
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approved
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