Abstract: Integrating an arbitrary polynomial function f of degree D over a general simplex in dimension n is well-known in the state of the art to be NP-hard when D and n are allowed to vary, but it ...

Polynomial integration is a fundamental principle in calculus with numerous applications in various fields like engineering, physics, computer science and economics. Despite its numerous applications, ...

To integrate the product of a polynomial and a function, apply term-by-term integration using techniques like integration by parts. For a polynomial $$ P(x) = a_nx^n + \dots + a_1x + a_0 $$ and ...

This project implements Monte Carlo integration for polynomial functions. Monte Carlo integration is a numerical method for estimating the value of definite integrals by generating random samples from ...

For 𝛼, 𝛽 ∈ ℕ₀ and max{𝛼, 𝛽} > 0, it is shown that the integrals of the Jacobi polynomials∫0t(t−0) δPn(α12,β12)(cosθ)(sinθ2)2α(cosθ2)2βdθ>0for all 𝑡 ∈ (0, 𝜋] and 𝑛 ∈ ℕ if 𝛿 ≥ 𝛼 + 1 for 𝛼, 𝛽 ...

Investigating modern gravity and cosmology models involves a stage of analyzing associated nonlinear dynamical systems. In general, such systems are not integrable, but they often admit additional ...

The coherent‐state representation of quantum‐mechanical propagators as well‐defined phase‐space path integrals involving Wiener measure on continuous phase‐space paths in the limit that the diffusion ...