In a typical calculus course, students are exposed to many functions. Some have their origin in a field of study, while others are simply combinations of polynomials, trig functions, exponentials, and logs that are put together simply to have an interesting chain/power rule etc.
My question is this: Do you know of any functions that are common (or essential) in a field (Math/Physics/Chemistry/Biology/Engineering) that are not commonly discussed in calculus texts--or perhaps are not done justice in calculus texts?