b91839ef-db76-4642-9a05-6240b142b1a6 15 6 9 decimal

&[DATE] &[TIME] - &[FILENAME]

Степень полинома Pangkat polinomial Polynomial order n 3 :

Hermite/Rodrigues polynomials z n H 1 - (n^z 2^2 / exp * z 2^2 / - exp (z n diff * :

Hermite/Hermite polynomials z n H 1 - (k^n! (* (k! (n 2 k * - (! (* / 2 z * (n 2 k * -^* (k 0 n 2 / Floor sum :

T 1 el z n H :

k 1 : k n ≤ k k 1 + : T k 1 + el T k el (z diff k / : for

z D T :

Коэффициенты полинома Эрмита Koefisien polinomial Hermite Hermite polynomial coefficients 0 D 03 - 0141 mat

Корни полинома Эрмита Akar polinomial Hermite Roots of Hermite polynomial 0 D polyroots 0 1.73205080756888 - 1.73205080756888 31 mat

x 0 H x 1 H x 2 H x 3 H x 4 H x 5 H 6 1 sys

=========== Hermite/Hermite vs Hermite/Rodrigues =============

Hermite/Hermite polynomials n x Her 1 - (k^n! (* (k! (n 2 k * - (! (* / 2 x * (n 2 k * -^* (k 0 n 2 / Floor sum :

Hermite/Rodrigues polynomials z n H 1 - (n^z 2^2 / exp * z 2^2 / - exp (z n diff * :

β 12 sqrt sqrt / :

α 0.355328053887817 :

n 3 :

... wrt to order 'n' ... 1. The βx 0.840896415253715 seems constant. 2. The magnitude ratio varies wrt 'n' . 3. Hermite/Hermite is at least one of the solution(s) of the Hermite DE .

x n H α n β x * Her ( * 2 1 sys

12 sqrt sqrt / 0.840896415253715

n 2 α ≡ 0.5 ≡ 3 α ≡ 0.355328053887817 ≡ 0 Ai ≡ 4 α ≡ 0.25 ≡ 31 mat ≡