Caloric polynomial

In differential equations, the "m"th-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 "m"th-degree Hermite polynomial in "x".