# Notation: $\varphi$ and $\phi$

Is it bad style to use $\phi$ and $\varphi$ in the same paper (for different things, of course)?

I'd like to use $\phi$ for a function and $\varphi$ for a particular function value.

• If you ask me, yes, it's bad, it's like using $a$ and $\mathrm a$ to denote two different things. You could use $\Phi$ and $\varphi$, for example – 5xum Aug 27 '15 at 15:24
• I agree. How about $\phi$ and $\phi_0$ for the value? Or the same for $\varphi$. – Silvia Ghinassi Aug 27 '15 at 15:27
• I know a professor who, when out of variables, went to Lucky Charms. Clovers, crescents, stars, horseshoes, etc. – Akiva Weinberger Aug 27 '15 at 15:43
• I would use $\varphi$ rather than $\phi$, which in some context, could be confused with $\emptyset$, especially if you write on a blackboard. – J.-E. Pin Aug 27 '15 at 17:12
• I also suggest you look this over: oeis.org/wiki/Greek_alphabet – Robert Soupe Aug 28 '15 at 16:56

Yes, it is bad style. Not everyone are used to distinguishing mentally between these variants of lower-case phi, so making a distinction will make the paper harder to read. It would be akin to making a distinction between loop-tailed $g$ and open-tailed $g$ in otherwise the same typeface/style.

It will also make it harder for someone to quote and discuss your formulas and results if they're using a medium where one cannot easily distinguish the variants.

• Wholeheartedly agree. I can imagine this sort of detail causing lots of unnecessary confusion in a math class. – Robert Soupe Aug 28 '15 at 16:36

It is not uncommon to use the same letter from different fonts in the same paper to denote different things.

For example I could see easily somebody using $A_n$ for some matrix and $\mathfrak{A}_n$ for the alternating group on $n$ symbols.

Thus, I do not think there is something wrong in principle with using $\phi$ and $\varphi$ in the same paper. For example, you might want to have one phi for use as an angle and one for Euler's totient function.

However, your specific idea of having one as the function and the other as the value of the function strikes me as not so good, specifically as it will be hard to recall which is which. The idea proposed in a comment to rather use uper and lower case instead seems good.

• In total agreement, especially on your last paragraph. I think I’m a coauthor on a paper that uses $\pi$ and $\varpi$, but few recognize the latter as a pi. – Lubin Aug 27 '15 at 16:13