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If I am explaining the meaning of symbols in a formula, like:

..., where 'e' is [the/an] electron charge ([the/a?] charge of [the/an] electron), 'c' is [the] speed of light, 'k' is [the] Boltzmann constant...

Is there a rule to put the definite (or indefinite) article?

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e, c and k are all unique values: there is only one of each, so their definitions should be, well, definite.

In fact, even if your signs represent variables rather than constants, the values which they represent in any actual case are specific to that instantiation, so the definite article is used in defining them:

a2 + b2 = c2, where a and b are the lengths of the two sides of any specific right triangle and c is the length of its hypotenuse.

But these variables refer to many possible instantiations. There are, for instance, quite a few (NEdd, approximately 1080) electrons in the universe, all identical, each of which may serve as an instantiation upon which e may be observed, so no specific electron is intended in your definition

Consequently you should write:

..., where e is the charge on an electron, c is the speed of light, k is the Boltzmann constant ...

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    e is conventionally referred to as "the electron charge" (or "the elementrary charge") in the context of academic writing in physics, though your suggested wording would probably not raise many eyebrows either.
    – The Photon
    Commented Nov 12, 2013 at 20:04
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    @ThePhoton Well, I last studied physics and chemistry in 1966, which appears to be just when the usage changed! ): Commented Nov 12, 2013 at 20:17
  • @StoneyB Thanks for the answer and the 'Ngram Viewer' link - awesome.
    – magnetar
    Commented Nov 12, 2013 at 22:00

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