Here's an equation of the Fourier transform:

Fourier Equation
In the same equation image above, in the second line, is an equation I read from a paper. It seems that the

*a_n* and

*b_n* are turned into functions of

*A(u)* and

*B(u)* respectively, which depend on the variable

*u*, which is the frequency. There is also an additional

*2*pi* in the

*sin *and

*cos* functions.

In other words, the eventual equation can get to become:

New Equation
I don't understand several things in this new equation.

First, what are the* A(u)* and *B(u) *functions? Why do they depend on *u*?

Second, why is there a *2*pi* in the *sin *and *cos *functions? What do the *2*pi *mean?

Third, how does the new equation differ from the original equation?

\frac{a_0}{2} + \sum_{n=1}^\infty a_n \cos(nx) + b_n \sin(nx)

above line not rendered very well. Try

f(x) = a_0/2 + sum (from n = 0 to infinity)(a_n cos(nx) + b_n sin(nx)