Why can I only use some capital greek letters inside my equations?

Question

For example:

\begin{equation}
\delta % ok
\Delta % ok
\epsilon % ok
\Epsilon % error
\end{equation}

Answer 1

Uppercase epsilon is E.

\begin{equation}
\delta % ok
\Delta % ok
\epsilon % ok
E        % ok
\end{equation}

Answer 2

Well, my wild guess is that such macros are missing because CM has no such glyphs to begin with, Knuth's Greek is meant for use in math and not for running text and thus there were no point in duplicating glyphs that are visually indistinguishable from Latin counterparts.

Answer 3

Other answers have made this fairly clear: a capital epsilon is identical to a capital E, so there's no need for a separate LaTeX command. However, there is a point missing from the answers above. Roman letters (by which I mean letters from the Roman alphabet) are conventionally set italic in math mode, to make clearer the distinction between maths and text. But Greek letters are set upright by default (though some journals deviate), because there's no distinction that needs making (assuming you're not writing in Greek). So if you really want a capital epsilon, and you want a consistent look for all your capital Greek letters, you should use \mathrm{E}.

Answer 4

David's point is worth underlining:

So basically, nobody would use a capital epsilon in a formula because it'd be visually indistinguishable from E.

If you wanted to type something actually in Greek, then you would use one of the packages designed for that (search on CTAN for "greek" to get an idea of what's available). The Greek letters that are defined in unadorned LaTeX should not be viewed as letters but as mathematical symbols. So α should be viewed in the same regard as something like ≤. This is underlined by their appearance: just as "x" looks different in text and in maths, so "α" will look different in text and in maths. So the fact that "Α" (\Alpha) and the like are missing is simply because regarded as a symbol, it's just "A", and no-one would ever write \Alpha because they can just write A and the fact of calling it "Alpha" adds nothing. Compare this with "x" (x) and "×" (\times) where the different names actually mean something (variable versus operator).

So, in summary, if you want to type \Epsilon and the system complains then you are doing something wrong: either you are trying to type something in Greek without loading a proper Greek alphabet, or you are distinguishing in the source code something that will be indistinguishable in the actual document.

Answer 5

To quote from The LaTeX Companion (p. 527),

Those capital Greek letters not present in this table are the letters that have the same appearance as some Latin letter. Similarly, the list of lowercase Greek letters contains no omicron because it would be identical in appearance to the Latin o. Thus, in practice, the Greek letters that have Latin look-alikes are not used in mathematical formulas.

So basically, nobody would use a capital epsilon in a formula because it'd be visually indistinguishable from E.

If this bothers you, you could define the missing macros for Greek letters, e.g.

\newcommand{\Alpha}{A}
\newcommand{\Beta}{B}
\newcommand{\Epsilon}{E}

and so on.