Feynmann's Trick For Exponential Integrals
Table of Contents
Feynmann’s Trick For Exponential Integrals #
$$\int_0^{\infty} x^n e^{-tx} dx = \frac{n!}{t^{n+1}}$$
Where
- \(t\) is a constant, and
- \(n!\) is the Gamma function (does not require \(n\) to be an integer)
Feynmann’s trick involves “differentiating under the integral” which is a whole technique on its own, and the above formula is something that can be found using this technique. I found that formula particularly hard to find online, so I decided to write it up.