0f4c0210-fe26-4208-ada1-370ad5ce1eca 43 4 5 decimal

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

n 2 / Floor Floor ≡

n 4 :

Legendre as local assignment 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 * 11 line :

Rodrigues n x P 12 n^n! (* / x 2^1 - (n^(x n diff * :

Hello Jean, Seems the crash it is related with the name of the iterator argument of sum(). Until is not fixed you can cure it by renaming k in either one of L(x,n) or the for loop move on the variable k, press F8 and rename it at once), then you can evaluate safely.

last 'n' polynomial Ω 1 el n x L :

The expansion is OK for plotting. The last polynomial L(n,x) & P(n,x) are identical, though of different form.

Ω 35 x 2^* 6 - 7 x 2^* + (* + 8 / 11 mat

Rodrigues => same as Legendre but not as simple n x P 21 - 7 x 2^* + (* 71 - x 2^+ (* + (1 - 3 x 2^* + (* 42 x 2^* 1 - x 2^+ (* + 24 /

n x L n x P 2 1 sys

Rodrigues last polynomial T 1 el n x P :

T 21 - 7 x 2^* + (* 71 - x 2^+ (* + (1 - 3 x 2^* + (* 42 x 2^* 1 - x 2^+ (* + 24 / 11 mat

visible expansion   n ≤ 4 k 1 : k n ≤ k k 1 + : T k 1 + el T k el (x diff k / : for

x D T : 21 - 7 x 2^* + (* 71 - x 2^+ (* + (1 - 3 x 2^* + (* 42 x 2^* 1 - x 2^+ (* + 24 / x 1 - 71 - 2 x 2^* + x 2^+ (* + 71 - 2 x 2^* + (* + (* 2 / 1 - 721 - x 2^+ (* 3 x 2^* + 10 x 2^* + (* + 4 / 35 x * 2 / 358 / 51 mat

Coefficients 0 D 0.375 0 3.75 - 0 4.375 51 mat

r 0 D polyroots : 0.339981 - 0.339981 0.861136 - 0.861136 41 mat

Legendre last 'n' polynomial. A very nice and correct expansion
but not same at the kernel level. I found no way to instruct the
kernel to renew itself of the symbolic expansion. Hover in 
green to see Ω1 at the kernel level. Ω 1 el n x L : 35 x 2^* 6 - 7 x 2^* + (* + 8 / 11 mat

visible expansion   n ≤ 4
Install new counter 'μ' x d μ 1 : μ n ≤ μ μ 1 + : Ω μ 1 + el Ω μ el (x diff μ / : for Ω 21 line :

In d(x),the symbolic expansion is correct, algebraically identical to Rodrigues T(x) but it is NOT ISOLATED from L(n,x). I found no way to assign the symbolic d(x) to a new fnct. No way otherwise than ... ...............copy/paste => Spool to file = NFG !

x d 35 x 2^* 6 - 7 x 2^* + (* + 8 / 5 x * 3 - 7 x 2^* + (* 2 / 151 - 7 x 2^* + (* 4 / 35 x * 2 / 358 / 51 mat

! NO reconciliation !

x F 35 x 2^* 6 - 7 x 2^* + (* + 8 / 5 x * 3 - 7 x 2^* + (* 2 / 151 - 7 x 2^* + (* 4 / 35 x * 2 / 358 / 51 mat :

0 d #

0 F 0.375 0 3.75 - 0 4.375 51 mat

r 0 F polyroots : 0.339981 - 0.339981 0.861136 - 0.861136 41 mat

x f x d numden 11 line :

x f 1 el 35 x 2^* 6 - 7 x 2^* + (* + 8 / 5 x * 3 - 7 x 2^* + (* 2 / 151 - 7 x 2^* + (* 4 / 35 x * 2 / 358 / 51 mat

35 x 2^* 6 - 7 x 2^* + (* + 8 / 5 x * 3 - 7 x 2^* + (* 2 / 151 - 7 x 2^* + (* 4 / 35 x * 2 / 358 / 51 mat

0 f 1 el #

coeff x 0 : 35 x 2^* 6 - 7 x 2^* + (* + 8 / 5 x * 3 - 7 x 2^* + (* 2 / 151 - 7 x 2^* + (* 4 / 35 x * 2 / 358 / 51 mat 21 line :

coeff 0.375 0 3.75 - 0 4.375 51 mat

x C x d : (35 x 2^* 6 - 7 x 2^* + (* + 8 / 5 x * 3 - 7 x 2^* + (* 2 / 151 - 7 x 2^* + (* 4 / 35 x * 2 / 358 / 51 mat

x C x 0 : x d 21 line :

0 C #