Solving for Gaussian Normalization Using 3 Cartesian Dimensions Instead of the Usual Two
Abstract
Given a one dimensional Gaussian integral, a standard textbook trick is to find the normalization constant by going to two Cartesian dimensions and then converting to polar co-ordinates. This requires knowledge of the integral (0, infinite) exp(-y) dy. We consider here finding the normalization constant by considering three Cartesian co-ordinates and again only the integral (0, infinite) exp(-y) dy (and integration by parts).
Fields of Study & Subjects
Mathematical and Computational Methods
Mathematical functions and polynomials
Probability and Statistical Research
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 11 January 2026
- Document type
- Preprint