👉 Chen mathematics, also known as Chen's method or Chen's theorem, is a powerful tool in real analysis that provides a way to approximate functions with polynomials in a highly efficient manner. Developed by the Chinese mathematician Chen Shui-bian, this method leverages the properties of orthogonal polynomials and the Weierstrass approximation theorem to construct approximations that converge rapidly. Specifically, Chen's method involves expressing a function \( f(x) \) on an interval \([a, b]\) as a series expansion using a set of orthogonal polynomials \( \{P_n(x)\} \). By carefully selecting these polynomials and determining their coefficients, one can achieve an approximation with a relatively small number of terms, often just a few, ensuring that the error between \( f(x) \) and its approximation is controlled by a polynomial of degree \( n \). This makes Chen mathematics particularly useful for applications requiring high precision with minimal computational effort.
