Polyanalytic function theory extends the classical theory of holomorphic functions by encompassing functions that satisfy higher‐order generalisations of the Cauchy–Riemann equations. This broader ...

We investigate a practical and fast analytic framework for portfolio modeling and tail risk allocation using Hermite polynomials. This framework was first discussed in "An analytical framework for ...

This repository contains examples of partial sums of orthogonal polynomials, including Hermite, Charlier, and Lommel polynomials. Each example includes Maple code with detailed comments explaining the ...

Different aspects of mathematical finance benefit from the use Hermite polynomials, and this is particularly the case where risk drivers have a Gaussian distribution. They support quick analytical ...

Abstract: This paper considers interpolating matrix polynomials P(λ) in Lagrange and Hermite bases. A classical approach to investigating the polynomial eigenvalue problem P(λ) x = 0 is linearization, ...

Abstract: By using the three-term recurrence equation satisfied by a family of orthogonal polynomials, their asymptotic expressions and bilinear generating functions, we obtain quadrature formulas for ...