数学

数学

Beyond Euler’s Partition Identity: The Algebraic Link Between Integer Partitions and Bell Polynomials via Infinite Products

Every math enthusiast has, at some point, been captivated by the sheer beauty of Euler's Partition Identity. This theore...
2026.05.20
数学
数学

Proof that a Certain Infinite Product Relates to a Trigonometric Function

I managed to prove the formula\ that appear in the post with the help of the generative AI. I will be sharing the proof....
2026.05.13
数学
数学

The calculation of values of the Dirichlet beta function for positive odd numbers using the infinite product formula of the sine function

In this post, we will calculate the values of Dirichlet beta function for positive odd numbers. Definition of the Dirich...
2026.04.02
数学
数学

The partition L function

In this post, I will introduce the partition \(L\) function. DefinitionsLet \(n\) be a positive integer. Consider the sy...
2025.04.28
数学
数学

Some kind of partition zeta function

In this post, I will introduce the partition zeta function. Definition【Definition】Let \(n\) be a positive integer and \(...
2025.04.28
数学
数学

On the sum of signs of conjugacy classes of the symmetric group

In this post, I will prove that\ where \(n\) is a positive integer. NotesIf \(\sigma \in S_n\) and \(\sigma' \in S_n\) a...
2024.07.01
数学