
Find the Hermite Polynomials of order 2, 4 and 6.
Recall that the recurrence relations are given by
We have to evaluate these coefficients for k=2, k=4 and k=6, with initial conditions a0=1, a1=0.
When k=2,
while
Consequently all even coefficients other than a2 will be zero. Since a1=0, all odd coefficients will be zero, too. Thus
H2(t)=1-2t2.
When k=4,
Consequently all even coefficients other than a2 and a4 will be zero. Since a1=0, all odd coefficients will be zero, too. Thus
You can check that
[Back]
[Exercises]
[Next]
[Algebra]
[Trigonometry]
[Complex Variables]
[Calculus]
[Differential Equations]
[Matrix Algebra]
S.O.S MATHematics home page

1998-07-08
Copyright © 1999-2004 MathMedics, LLC. All rights reserved.
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA