<p> Collect roots </p>

a8612a0b-31d3-4387-b697-f0031d94885e 19 6 12 decimal

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

x y axes x y / - :

Poly order n 8 :

3 appVersion 0.98.6179 ≡

Legendre  in native algo mode n z L 1 - (k^2 n * 2 k * - (! (z n 2 k * -^* (* 2 n^k! (* n k - (! (n 2 k * - (! (* (* / (k 0 n 2 / Floor sum :

0 x L 1 x L 2 x L 3 x L 4 x L 5 x L axes 7 1 sys

r n x L 0 ≡ x 1 - 1 solve :

1 - (k^2 n * 2 k * - (! (z n 2 k * -^* (* 2 n^k! (* n k - (! (n 2 k * - (! (* (* / (k 0 n 2 / Floor sum 11 line

<p> Collect roots </p>

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

vx r : vy r 0 * : 12 mat char . : size 10 : clr black : 13 mat data vx vy augment : roots data char size clr plot : 41 sys

roots n x L 2 1 sys

r 0.96 - 0.797 - 0.526 - 0.183 - 0.183 0.526 0.797 0.96 81 mat

can't use 'k' μ 9 :

n 1 μ range Lpoly n 1 + el n x L : Lpoly 1 el 1 : 21 line for

Lpoly 1 x 1 - 3 x 2^* + 2 / x 3 - 5 x 2^* + (* 2 / 35 x 2^* 6 - 7 x 2^* + (* + 8 / x 157 x 2^* 10 - 9 x 2^* + (* + (* 8 / 5 - 21 x 2^* 5 x 2^15 - 11 x 2^* + (* + (* + 16 / x 35 - 3 x 2^* 10511 x 2^* 21 - 13 x 2^* + (* + (* + (* 16 / 353 x 2^* 420 - 11 x 2^* 21013 x 2^* 28 - 15 x 2^* + (* + (* + (* + 128 / x 31511 x 2^* 420 - 13 x 2^* 1265 x 2^* 36 - 17 x 2^* + (* + (* + (* + (* 128 / 101 mat

j 9 :

Select poly in range j ≤ μ

Lpoly j el 2 1 sys