This article discusses the general theory of self-reciprocal functions in the Fourier transform, particularly focusing on the eigenspaces of the Fourier transform.

As an example of a self-reciprocal function in the Fourier transform, we introduce |t|^(-1/2).

Basic concepts of the Mellin transform.

Calculate the Gaussian integral using the Wallis integral.

This article discusses Wallis’ formula, which provides an approximation of the intermediate binomial coefficients.