Fourier transformation formula confusion

Question

I found two formulas for Fourier transformation , which one is correct.

1. $$ F[f(x)]=\frac {1}{\sqrt {2\pi}} \int_{-\infty}^\infty f(x)e^{ipx} dx $$

2. $$ F[f(x)]= \int_{-\infty}^\infty f(x)e^{ipx} dx $$

Or if both are correct where to use which formula?

Answer 1

The two formula only differ by a constant factor, which is really unessential. Other conventions exist, with an exponent $i2\pi px$ rather than $ipx$, and the choice is mainly a matter of taste and convenience.

In addition, many problems are solved by taking direct transforms followed by inversion, and the constant factor just vanishes. So you shouldn't worry much: the first computation you will write will make it clear which definition you use. And you are always free to state it explicitly.