What's the difference between $F(x)$ and $f(x)$? (There is a question similar to mine, but it talks about f[x] and F[x].)
I've seen some people use F(x) when denoting functions, but what is the difference between using a capital F and a lower case f?
 A: It is sometimes used to denote the antiderivative, but generally there is none. It doesn't matter if you write $f(x)=$ or $F(x)=$ or $\mu(x)=$ or if you use a small picture of a house. You're just choosing what symbol represents the function, it's what comes after the $=$ sign that matters.
A: Well, there is absolutely no difference if you are going by notations of functions. But then special meanings are associated with capital and small letters to denote functions and these meanings vary from one field to another. For instance, in statistics, F(x) and f(x) mean two different functions. F(x) represents the cumulative distribution function, or cdf in short, of a random variable as opposed to f(x) which represents the probability density function, or pdf,  of the continuous random variable.
A: It really depends on the application and field of mathematical study and how the standard notation is set out.
I could declare a function f(x) and a function g(x), I could call it whatever i so desire.  When working on integrals however, if I integrate f(x), I may choose to call the result F(x).  I think the use of capital letters also occurs when working with Fourier Transforms and Laplace Transforms.
A: There is no difference. It's a matter of preference. For all you care you could have function $\heartsuit(x)$.
