Stirling's formula finds a relationship of n!,nⁿ,eⁿ while n trends to infinity.

## Posts of MATHEMATICS

### The Stirling Formula

### Box-Muller Transformation

The Box-Muller transformation is a method to construct a random variable that follows a Gaussian distribution by using a random variable that follows a uniform distribution.

### Linear Congruential for Pseudorandom Number

Linear congruential method is a pseudo-random number generation method that generates a random number sequence based on a deterministic mathematical algorithm.

### The Laplace Theorem for Determinant

Laplace's theorem in determinants and its applications

### The Problem of Weighing Coins with Balance.

The 'Coin Weight Problem' aims to solve the following mathematical problem: Among N coins, one coin has a different weight. with a balance scale, ensure finding the different coin with the fewest number of weighings.

### The Introduction to Bernoulli Number

Introduction, derivation and proof of Bernoulli numbers

### Equivalence of Rectangular and Trapezoidal Approximations

Discusses the equivalence and error estimation in integrating piecewise continuous functions using rectangular and trapezoidal approximations.

### Taylor Formula, Taylor Theorem, Taylor Series, Taylor Expansion

This article mainly introduces the content and connection between the four concepts of Taylor's formula, Taylor's theorem, Taylor series and Taylor's expansion.

### Proof of Faulhaber's Formula

Faulhaber's Formula, which provides a method to compute the sum of the p-th powers of the first n positive integers.

### The Catalan Series

The article discusses Catalan numbers, a sequence used in combinatorial problems. It covers their recurrence relation, closed form, and applications in path counting. It provides insights into problem-solving using Catalan numbers.