~v200 200 ~w154 4 408 779 0 283 0 0 ~f? 14 12 10
? 2 1 1 0 ? ? ? "Arial" ? ? ? 0 ? 0 1
"Times" 12 ? ? 5 0 c n 100 0 0 0 k 288
i"CHEBYCHEV"
-2 1 26177 26178 26115 26178 1 1 1 1 0 0
0 0 -1 0 1 -1 -1 -1 -1 -1 1 1 ? ? 
~Q
]|Expr|[#b @`bb#_b#_b#_})!# b&,["! )'# b&," *|: ;bP8&c0!)Chebyshev|
  | and Legendre Polynomials}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b&,|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~V?v0 (P)~p0
1 ~V?v0 (T)~p0
1 ~V?c0 (n)~p0
1 ~V?v0 (y)~p0
1 ~V?v0 (x)~p0
1 ~V?f273 (arccos)~p0
1 ~V?f257 (cos)~p0
1 ~Q
]|Expr|[#b @`bb#_b#_b#_}`f#})!# b$@["! ) # b$@|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}))# b$@" *|: ;bP8&c0!*Chebyshev|
  | polynomial of degree n}& b!( b"0 b#8 b$@ b%H b&P!WW}}|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
0 ~A(T_n=cos(n*arccos(x)))~p0
1 ~d~Q
]|Expr|[#b @`bb#_b#_b#_}`fb#@})!# b$@["! ) # b$@|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}))# b$@" *|: ;bP8&c0!*Legendre |
  |polynomial of degree n}& b!( b"0 b#8 b$@ b%H b&P!WW}}|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
0 ~Ht(P_n):(1/(2^n*n!)*((Diff(x))^n*(x^2-1)^n))~p0
1 ~A(P_n)~p1
1 ~A(P_n=2.5*x^3-1.5*x)~p0
255 ~d~sb/_!!   }
"&!  c#T"!c"H#_c/__c/__}
^ _~A(P_n=1/(2^n*n!)*(Diff(~
 x))^n*(x^2-1)^n)~p0
2 ~sb/^!!   }
#'!  c#T"!c%\"_c/__c/__!}
^ _~A(P_n=0.020833333333333332*~
 (Diff(x))^3*(x^2-1)^3)~p0
3 ~sb/_!!   }
$&!  c#T"!c"H#_c/__c/__}
^ _~Q
]|Expr|[#b @`bb#_b#_b#_}) # b$@}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
0 ~Q
]|Expr|[#b @`bb#_b#_b#_})## b!," *|: ;bP8&c0!*Input n|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
0 ~A(n=3)~p0
255 ~d~G1 1 161 386
1 1 4 3 10
(-1.1000000000000001...1.1000000000000001):(~
 -1.1000000000000001...1.1000000000000001):(n=0...16):(1):(16)~
 ~Q
]|Expr|[#b @`bb#_b#_b#_}`f#})## b$@" *|: ;bP8&c0!*Chebyshev polynomial|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~L1 255 ? (x,T_n):(x=-1...1)~p0
1 ~gc0 62 ? 0 -3724 -3724 0
1170 -3591 -2583 0
3120 -3369 -925 0
5201 -3133 529 0
7411 -2881 1743 0
9362 -2660 2551 0
10272 -2556 2850 0
11442 -2423 3164 0
12482 -2305 3382 0
13653 -2172 3560 0
14563 -2069 3652 0
15213 -1995 3694 0
15603 -1951 3711 0
16513 -1847 3723 0
17684 -1714 3689 0
18724 -1596 3615 0
19455 -1513 3540 0
19894 -1463 3486 0
20235 -1424 3439 0
20804 -1360 3354 0
21845 -1241 3172 0
22755 -1138 2988 0
23925 -1005 2722 0
24965 -887 2459 0
26135 -754 2138 0
27046 -650 1871 0
28086 -532 1553 0
28996 -429 1263 0
30166 -296 879 0
31207 -177 530 0
32377 -44 133 0
33287 59 -177 0
34327 177 -530 0
35238 281 -836 0
36408 414 -1221 0
37448 532 -1552 0
38618 665 -1910 0
39529 768 -2174 0
40569 887 -2459 0
41479 990 -2690 0
42649 1123 -2960 0
43690 1241 -3172 0
44860 1374 -3374 0
45770 1478 -3502 0
46810 1596 -3615 0
47378 1660 -3661 0
47720 1699 -3682 0
48159 1749 -3704 0
48891 1832 -3722 0
49931 1950 -3711 0
50369 2000 -3692 0
51101 2083 -3641 0
52011 2187 -3544 0
53052 2305 -3382 0
53962 2409 -3195 0
56172 2660 -2551 0
57343 2793 -2095 0
58253 2896 -1681 0
60203 3118 -611 0
62414 3369 924 0
64364 3591 2582 0
65535 3724 3724 0
~
 ~Q
]|Expr|[#b @`bb#_b#_b#_}`fb#@})## b$@" *|: ;bP8&c0!*Legendre |
  |polynomial}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~L1 16711680 ? (x,P_n):(x=-1...1)~p0
1 ~gc0 71 ? 0 -3724 -3724 0
1170 -3591 -2961 0
2080 -3487 -2416 0
3120 -3369 -1841 0
4030 -3266 -1381 0
5201 -3133 -844 0
6241 -3014 -417 0
7411 -2881 9 0
8321 -2778 301 0
9362 -2660 597 0
10272 -2556 822 0
11442 -2423 1069 0
12482 -2305 1249 0
13653 -2172 1410 0
14563 -2069 1507 0
15603 -1951 1588 0
16513 -1847 1634 0
17244 -1764 1656 0
17409 -1745 1659 0
17684 -1714 1663 0
18074 -1670 1665 0
18724 -1596 1661 0
19894 -1463 1630 0
20804 -1360 1586 0
21845 -1241 1517 0
22200 -1201 1489 0
22413 -1177 1471 0
22755 -1138 1441 0
23193 -1088 1400 0
23925 -1005 1324 0
24965 -887 1204 0
26135 -754 1053 0
28996 -429 629 0
31207 -177 265 0
32377 -44 67 0
33287 59 -89 0
34327 177 -265 0
35238 281 -417 0
38618 665 -944 0
39529 768 -1071 0
40179 842 -1156 0
40569 887 -1204 0
40910 925 -1245 0
41265 966 -1286 0
41479 990 -1310 0
41917 1040 -1357 0
42649 1123 -1429 0
43690 1241 -1517 0
44860 1374 -1593 0
45770 1478 -1635 0
46810 1596 -1661 0
47378 1660 -1665 0
47720 1699 -1664 0
47994 1730 -1661 0
48159 1749 -1659 0
48891 1832 -1639 0
49931 1950 -1588 0
51101 2083 -1495 0
52011 2187 -1395 0
53052 2305 -1249 0
53962 2409 -1094 0
55132 2541 -852 0
56172 2660 -597 0
57343 2793 -262 0
58253 2896 36 0
60203 3118 787 0
61374 3251 1318 0
62414 3369 1841 0
63584 3502 2490 0
64364 3591 2960 0
65535 3724 3724 0
~
 ~Q
]|Expr|[#b @`bb#_b#_b#_})%# b$@" *|: ;bP8&c0!*axes and grids|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~R5592405 ? (x,y):(y=bottom...top):(x=left...right):(0)~p0
1 ~gc1 2 ? 0 -3724 -4096 0
65535 -3724 4096 0
~gc1 2 ? 0 -1862 -4096 0
65535 -1862 4096 0
~gc1 2 ? 0 0 -4096 0
65535 0 4096 0
~gc1 2 ? 0 1862 -4096 0
65535 1862 4096 0
~gc1 2 ? 0 3724 -4096 0
65535 3724 4096 0
~
 ~R5592405 ? (x,y):(x=left...right):(y=bottom...top):(0)~p0
1 ~gc1 2 ? 0 -4096 -3724 0
65535 4096 -3724 0
~gc1 2 ? 0 -4096 -1862 0
65535 4096 -1862 0
~gc1 2 ? 0 -4096 0 0
65535 4096 0 0
~gc1 2 ? 0 -4096 1862 0
65535 4096 1862 0
~gc1 2 ? 0 -4096 3724 0
65535 4096 3724 0
~
 ~X1 0 (x,0):(x=left...right):(x)~p0
1 ~gc1 2 ? 0 -4096 0 0
65535 4096 0 0
~X2 0 (0,y):(y=bottom...top):(~
 y)~p0
1 ~gc1 2 ? 0 0 -4096 0
65535 0 4096 0
~Q
]|Expr|[#b @`bb#_b#_b#_})!# b$@" *|: ;bP8&c0!*declarations|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~V?c64 (left)~p0
1 ~V?c65 (right)~p0
1 ~V?c66 (bottom)~p0
1 ~V?c67 (top)~p0
1 ~t~p0
1 ~c1
13 -1 15 -1 ~c2
14 -1 12 -1 11 -1 ~c3
15 -1 14 -1 18 -1 3 -1 ~e