<p> plotG(vx,vy,a,b,c) </p>

20d82bfc-297e-47fc-ae6f-b8442a32ce0d 9 4 5 decimal

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

vx vy a b c plotG a char ≡ b size ≡ c color ≡ 13 mat n vx length : plot vx 1 el vy 1 el a b c augment : i 2 n range plot plot vx i el vy i el a b c augment stack : for plot 51 line :

n x T n x acos * cos :

ChebyShev Polynomials

N 7 :

m 0 N range :

n N 1 + :

Plot roots of ChebyShev roots m 0 N range x m 1 + el 0 m * : Z m 1 + el 2 m * 1 + 2 N 1 + (* / π * cos : 21 line for Z x augment 21 line :

roots 0.9808 0 0.8315 0 0.5556 0 0.1951 0 0.1951 - 0 0.5556 - 0 0.8315 - 0 0.9808 - 082 mat

vx roots 1 col : vy roots 2 col : r vx vy . 12 black plotG : 31 line

3 x T n x T r 3 1 sys

ChebysShev polynomial form ... expand in vector function n x Tc 1 n 0 ≡ n 2 / 1 - (j^n j - / n j - (! j! (n j - (j - (! * / * 2 x * (n 2 j * -^* j 0 n 2 / Floor sum * cases 11 line :

n 16 range T 1 el 1 : T n 1 + el n x Tc : 21 line for

T 1 x 2 x 2^* 1 - x 3 - 4 x 2^* + (* 8 x 2^* 1 - x 2^+ (* 1 + x 54 x 2^* 5 - 4 x 2^* + (* + (* 1 - 2 x 2^* 98 x 2^* 3 - 2 x 2^* + (* + (* + 71 mat