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 = −1/2, this polynomial reduces to the mth-degree Hermite polynomial in x.
References . Contains an extensive bibliography on various topics related to the heat equation.
External links
Zeroes of complex caloric functions and singularities of complex viscous Burgers equation