Caloric Polynomial

In differential equations, the mth-degree caloric polynomial (or heat polynomial) is a "parabolically m-homogeneous" polynomial P_m(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.