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Some letters of the greek alphabet include alternative letters. For instance, we have \Phi, \phi and \varphi.
What is the purpose of the variant versions of these letters? Why are these not available for the entire greek alphabet?
Information about these symbols: https://en.wikibooks.org/wiki/LaTeX/Mathematics#Greek_letters. The Comprehensive LaTeX Symbol List from CTAN does not mention their purpose either.
First, the difference between \Phi and \phi corresponds to the upper and lower cases of the letter. It is available for almost all the greek letters (the ones that are different from the latin uppercase).
There are however more alternative forms for specific letters; these alternative forms are available for the most common glyph variants of the greek letters. The use of one or the other is then either aesthetic or a question of norms/habits in a field (\varpi tends to be used for example for some variables in physics, and its meaning is completely different from the classical meaning of \pi).
\varphi is more used than \phi.
\Alpha for example since it just looks like A.
\varphi is usually used for an angle (e.g. in spherical coordinates, where also \vartheta is used instead of \theta) while \phi is used for phases
Aug 23, 2013 at 11:49
The variant letters are not introduced for the purpose of mathematical notation; they are alternate forms of those letters, as they were written by Greek scribes. See the Wikipedia article for the Greek alphabet, especially the sections on its history and letter shapes.
