feat(ring_theory/polynomial): add properties of `coeff (hermite n)` (#18837)
Added lemmas showing recursive relations between coefficients of `polynomial.hermite n`:
- `coeff (hermite (n + 1)) 0 = -(coeff (hermite n) 1)`
- `coeff (hermite (n + 1)) (k + 1) = coeff (hermite n) k - (k + 2) * (coeff (hermite n) (k + 2))`
Showed some more properties of the coefficients of Hermite polynomials:
- for `k>n`, the `k`th coefficient of the `n`th Hermite polynomial is zero
- the `n`th Hermite polynomial is of degree `n`
- the Hermite polynomials are monic
Co-authored-by: Jake Levinson [levinson.jake@gmail.com](mailto:levinson.jake@gmail.com)
Co-authored-by: lukemantle <62187700+lukemantle@users.noreply.github.com>
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>