Caloric polynomial (original) (raw)

In differential equations, the mth-degree caloric polynomial (or heat polynomial) is a "parabolically m-homogeneous" polynomial Pm(x, t) that satisfies the heat equation "Parabolically m-homogeneous" means The polynomial is given by It is unique up to a factor. With t = −1, this polynomial reduces to the mth-degree Hermite polynomial in x.