$f(x) = 2\pi r [\;\text{complicated formula}\;]$

The simple $2\pi r$ term is carried through from beginning to end unchanged, and I'd like to omit it from the function definition to avoid unnecessary clutter in the derivation. Basically, I want to define a new function name that excludes the $2\pi r$ part. I could give it a totally different name, like $g(x)$, such that $f(x)=2\pi r \; g(x)$, but I'd rather keep the $f(x)$ function name and just add some character modifier such as a prime symbol, or something like that. Is there some kind of convention for this? Since the prime symbol usually denotes differentiation, I'm thinking that wouldn't be a good choice. Maybe a subscript?