A082726 Continued fraction expansion of current estimate of the fine-structure constant alpha.

0, 137, 27, 1, 3, 1, 1

Offset: 0

Author

N. J. A. Sloane, May 21 2003

Keywords

• nonn
• cofr
• hard
• more

Comments

The estimate is continually changing.

The term a(7) is today known to be in between 15 and 17, but most likely equal to 16.

The value refers to the zero-energy limit of the coupling constant. At higher energies the value increases; e.g. at the energy 90 GeV of the Z-boson, it is about 1/128.

a(7) is believed to be 17 or 18 according to the revised 2014 CODATA value. - Charles R Greathouse IV, Sep 13 2017

Examples

			CODATA 2014: alpha = 0.007 297 352 5664(17) = 1 / 137.035 999 139(31), where values in parentheses indicate uncertainty in the preceding 2 digits.
		

Links

• NIST, fine-structure constant
• NIST, inverse fine-structure constant
• Wikipedia, Fine-structure constant.

Crossrefs

Cf. A005600.

Formula

alpha = e^2*c*mu/2h, where e ~ 1.602e-19 is the elementary charge, c = 299792458 m/s the speed of light, mu = pi*4e-7 H/m the vacuum permeability, and h ~ 6.626e-34 Planck's constant.