cp's OEIS Frontend

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.

Showing 1-3 of 3 results.

A003673 Decimal expansion of fine-structure constant alpha.

Original entry on oeis.org

0, 0, 7, 2, 9, 7, 3, 5, 2, 5, 6
Offset: 0

Views

Author

N. J. A. Sloane, Mira Bernstein

Keywords

Examples

			alpha = 7.29735256... * 10^-3 = 0.00729735256...

References

  • John Barrow, The Constants of Nature, 367pp, Jonathan Cape, 2002.
  • H. J. Fischbeck and K. Fischbeck, Formulas. Facts and Constants, Springer-Verlag, NY, 2nd ed., 1987.
  • K. R. Lang, Astrophysical Data: Planets and Stars, Springer-Verlag, NY, 1991.
  • Martin J. Rees. Just Six Numbers: the deep forces that shape the universe. Phoenix. 1999
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A005600, A082726.

Programs

  • Mathematica
    UnitConvert[Quantity["FineStructureConstant"]] (* requires Mathematica 9+; Andrey Zabolotskiy, Aug 15 2016 *)

Formula

alpha = e^2/(4*Pi*E*h*c), where e is the elementary charge (A081823), E is the electric constant (A081799), h is the reduced Planck constant (A254181), c is the speed of light (A003678). - Ilya Gutkovskiy, Jul 27 2016
alpha = V_n1/c = A081800/A003678. - Omar E. Pol, Mar 11 2018

Extensions

Updated May 20 2003
Updated by Omar E. Pol, Aug 09 2009, R. J. Mathar, Dec 15 2012
Updated by Arkadiusz Wesolowski, Feb 08 2016
Definition edited by N. J. A. Sloane, Feb 11 2016

A005600 Decimal expansion of reciprocal of fine-structure constant alpha.

Original entry on oeis.org

1, 3, 7, 0, 3, 5, 9, 9, 9
Offset: 3

Views

Author

N. J. A. Sloane, Mira Bernstein

Keywords

Comments

The fine-structure "constant" actually isn't a constant, it depends on the energy at which it is measured: Its value is known to approach 1/128 at interaction energies above 80 GeV. For other considerations, e.g., whether the value of the fine-structure constant differs by location and over time, see the Wikipedia article or other links. - M. F. Hasler, Oct 30 2013

Examples

			1/alpha = 137.035999206(11) [Morel et al., 2020]

References

  • John Barrow, The Constants of Nature, 367 pp., Jonathan Cape, 2002.
  • K. R. Lang, Astrophysical Data: Planets and Stars, Springer-Verlag, NY, 1991.
  • Martin J. Rees, Just Six Numbers: the deep forces that shape the universe, Phoenix, 1999.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A003673, A082726.

Formula

1/alpha = 1/A003673.
1/alpha = c/V_n1 = A003678/A081800. - Omar E. Pol, Mar 11 2018

Extensions

Updated May 20 2003
Updated by Omar E. Pol, Aug 09 2009
Updated by Raphie Frank, Dec 13 2012
Updated by Arkadiusz Wesolowski, Feb 08 2016
Updated by Rémy Sigrist, Dec 05 2020
Dropped the digits that could change with 1 standard error variation of the value provided by CODATA - Andrey Zabolotskiy, Dec 12 2020

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

Original entry on oeis.org

0, 3, 3, 3, 4, 9, 3, 1, 2
Offset: 0

Views

Author

Chase Roycroft, Aug 19 2021

Keywords

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

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.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.