Definition:Hermite Polynomial

Definition

A Hermite polynomial is a polynomial which satisfies the differential equation:

$\dfrac {\d^2 y} {\d x^2} = 2 x \dfrac {\d y} {\d x} + 2 n y = 0$

Such a polynomial is of the form:

$\paren {-1}^n \map \exp {x^2} \map {\dfrac {\d^n} {\d x^n} } {\map \exp {-x^2} }$

Also see

• Results about Hermite polynomials can be found here.

Source of Name

This entry was named for Charles Hermite.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Hermite polynomial
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Hermite polynomial