in fact has the same leading coefficient (the asymptotic growth is unchanged). Indeed, if denotes the (physicist's) Hermite polynomial of degree , then the Weierstrass transform of is simply . This can be shown by exploiting the fact that the generating function for the Hermite polynomials is closely related to the Gaussian kernel used in the definition of the Weierstrass transform.

Exponentials, Sines, and Cosines