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

An overview of Gray code.

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

Basic concepts of the Mellin transform.

On the pursuit of truth and the importance of making concepts understandable to others.

Calculate the Gaussian integral using the Wallis integral.

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

An overview of Fresnel integrals.

Discusses various conventions for defining the Fourier transform.

Calculating Fourier transform of the probability density function of the normal distribution.

This text describes the Cantor set, a null set with the cardinality of the continuum.

Deriving the equation of an ellipse.

Find the family of curves that are orthogonal to a family of parabolas.

An explanation of the solution to the Basel Problem.

Although this is a basic problem, calculating the average of angles can be tricky and prone to mistakes. This article explains how to correctly find the average angle.

I calculated the expected value of the cosine of a random variable following the standard normal distribution.