Definition:Hermite Polynomial
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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