- The Hermite polynomials
are solutions to the Hermite differential equation of the form
where
,
and
(positive integer parameter k)
is a solution of the Hermite equation. Therefore, defining
.
- A natural one to define Hermite polynomials is through the so-called Rodrigues'formula:
- The first few Hermite polynomials are given by
- Recursion relation:
Example py-file: The program to find first 6 Hermite polynomials:
myHermite.py
Figure 5.18:
First 6 Hermite Polynomials
with Recursion Relation:
.
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Figure 5.19:
Plot of first 6
.
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Subsections