Reliable Gauss-Hermite Numerical Integration Source Code from International Sources

The following presents source code for Gauss-Hermite numerical integration, which has gained widespread international recognition for its reliability and accuracy. This implementation utilizes the Gauss-Hermite quadrature formula - a mathematical approach specifically designed for computing integrals involving exponential-weight functions, particularly effective for integrals of the form ∫e^(-x²)f(x)dx. In computational mathematics, this algorithm is particularly valuable for numerical integration problems commonly encountered in quantum physics, statistical mechanics, and probabilistic computations. The code structure typically includes key components: node and weight calculation using Hermite polynomial roots, function evaluation at predetermined quadrature points, and weighted summation for integral approximation. This source code provides a solid foundation for implementing Gauss-Hermite numerical integration in computational projects, featuring modular design that allows for straightforward modification of integration parameters, function definitions, and precision requirements to suit specific application needs.