c6751d89-b4a8-4f62-84b1-c81c9d0f60f2 13 4 5 decimal

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Legendre coefficients & roots

Legendre last 'n' polynomial n x L 12 n^/ 1 - (k^2 n * 2 k * - (! (* k! (n k - (! (* n 2 k * - (! (* / x n 2 k * - (^* k 0 n 2 / Floor sum * :

n 2 / Floor Floor ≡

n 8 :

last 'n' polynomial => copy/paste in Ω1 n x L 353 x 2^* 420 - 11 x 2^* 21013 x 2^* 28 - 15 x 2^* + (* + (* + (* + 128 /

Smath 6179 does not accept Ω1:=L(n,x) in lieu: copy/paste. Counter μ ≠ n,k

Ω 1 el 353 x 2^* 420 - 11 x 2^* 21013 x 2^* 28 - 15 x 2^* + (* + (* + (* + 128 / :

μ 1 : μ n ≤ μ μ 1 + : Ω μ 1 + el Ω μ el (x diff μ / : for x d Ω : 21 line

0 d equate to collect ≡

r 0 d polyroots :

R i 1 r rows range p i el . : for i 1 r rows range zero i el 0 : for r zero p augment 31 line :

R n x L 2 1 sys

R 0.1834 - 0 . 0.1834 0 . 0.5255 - 0 . 0.5255 0 . 0.7967 - 0 . 0.7967 0 . 0.9603 - 0 . 0.9603 0.83 mat

plot 0 x L 1 x L 2 x L 3 x L 4 x L 5 x L 61 sys :

plot