~v200 200 ~w157 4 393 730 0 373 0 74 ~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$@" *|: ;bP8&c0!)Recursive Chebyshev|
  | Polynomials}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~V?f0 (T)~p0
1 ~V?f273 (arccos)~p0
1 ~V?f257 (cos)~p0
1 ~V?v0 (k)~p0
1 ~V?v0 (n)~p0
1 ~V?v0 (y)~p0
1 ~V?v0 (x)~p0
1 ~V?c1 ('p)~p0
1 ~Q
]|Expr|[#b @`bb#_b#_b#_})## b!," *|: ;bP8&c0!*Input n|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
0 ~A(n=3)~p0
255 ~d~A(T(?n,?x)=Conditional(1,(?n=0);?x,(?n=1);2*?x*T(?n-1,?x)-~
 T(?n-2,?x),(?n>1)))~p0
0 ~d~Q
]|Expr|[#b @`bb#_b#_b#_})!# b$@["! ) # b$@|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW})%# b$@" *|: ;bP8&c0!*Chebyshev|
  | Polynomial Plot}& b!( b"0 b#8 b$@ b%H b&P!WW}}|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
0 ~G1 1 161 386
1 1 4 3 10
(-1.1000000000000001...1.1000000000000001):(~
 -1.1000000000000001...1.1000000000000001):(n=0...16):(1):(16)~
 ~Q
]|Expr|[#b @`bb#_b#_b#_}`f#})!# b$@" *|: ;bP8&c0!*polynomial|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~L1 255 ? (x,T(n,x)):(x=-1...1)~p0
1 ~gc0 59 ? 0 -3724 -3724 0
3120 -3369 -925 0
4030 -3266 -250 0
6241 -3014 1141 0
7411 -2881 1743 0
9362 -2660 2551 0
9930 -2595 2743 0
10143 -2571 2810 0
10436 -2538 2898 0
10710 -2507 2976 0
11706 -2393 3225 0
12305 -2325 3349 0
13262 -2217 3508 0
13994 -2133 3599 0
14349 -2093 3634 0
14563 -2069 3652 0
15213 -1995 3694 0
15944 -1912 3720 0
16870 -1807 3719 0
17684 -1714 3689 0
18074 -1670 3666 0
19894 -1463 3486 0
20235 -1424 3439 0
21845 -1241 3172 0
22413 -1177 3060 0
22541 -1162 3034 0
22755 -1138 2988 0
23193 -1088 2893 0
23925 -1005 2722 0
24965 -887 2459 0
27046 -650 1871 0
27696 -576 1674 0
28086 -532 1553 0
28996 -429 1263 0
38618 665 -1910 0
42649 1123 -2960 0
43690 1241 -3172 0
44990 1389 -3394 0
45770 1478 -3502 0
46146 1520 -3547 0
46373 1546 -3572 0
46749 1589 -3609 0
47378 1660 -3661 0
47720 1699 -3682 0
48583 1797 -3717 0
49473 1898 -3721 0
50095 1969 -3705 0
50369 2000 -3692 0
51101 2083 -3641 0
52011 2187 -3544 0
53052 2305 -3382 0
53962 2409 -3195 0
56336 2678 -2492 0
57444 2804 -2051 0
59293 3014 -1142 0
61374 3251 158 0
62414 3369 924 0
63584 3502 1884 0
65535 3724 3724 0
~
 ~Q
]|Expr|[#b @`bb#_b#_b#_}`fb#@})!# b$@" *|: ;bP8&c0!*roots|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1
0 ~S17 ? 16711680 ? ? (cos((2*k-1)/(2*n)*'p),0):(k=1...n):(8)~p0
1 ~gc-1 3 ? 0 3225 0 0
24575 0 0 0
40960 -3225 0 0
~Q
]|Expr|[#b @`bb#_b#_b#_})%# b$@" *|: ;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$@ b%H b&P!WW}]|[~p1
0 ~V?c64 (left)~p0
1 ~V?c65 (right)~p0
1 ~V?c66 (bottom)~p0
1 ~V?c67 (top)~p0
1 ~t~p0
1 ~T~Q
]|Expr|[#b @`bb#_b#_b#_})!# b$R" *|: ;bP8&c0!*Examples|
  |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0
0 ~Ht(T_?n(?x)):(Conditional(1,(?n=0);?x,(?n=1);2*?x*T_(?n-1)(?x)-~
 T_(?n-2)(?x),(?n>1)))~p0
1 ~A(T_4(x))~p1
0 ~A(T_4(x)=8*x^4-8*x^2+1)~p0
255 ~sb/_!!   }
"&!  c#T"!c"L#_c/__c/__}
^ _~A(T_4(x)=2*x*T_3(x)-~
 T_2(x))~p0
1 ~sb/^!!   }
#'!  c#T"!c#L"_c/__c/__!}
^ _~A(T_4(x)=2*x*(2*x*T_~
 2(x)-T_1(x))-(2*x*T_1(x)-T_0(x)))~p0
2 ~sb/_!!   }
#+!  c#T"!c"L" c"H#"c#L"_c/__c/__!}
#+!  c#T"!c"L"!c"T! c#L"_c/__c/__!}
^ _~
 ~A(T_4(x)=4*x^2*T_2(x)-4*x*T_1(x)+T_0(x))~p0
3 ~sb/_!!   }
"&!  c#T"!c"L"_c/__c/__}
^ _~A(T_4(x)=4*x^2*(2*x*~
 T_1(x)-T_0(x))-4*x*x+1)~p0
4 ~sb/_!!   }
#+!  c#T"!c"L# c"H#"c#L"_c/__c/__!}
#-!  c#T"!c"L#!c"T! c"H#"c#L"_c/__c/__!}
#)!  c#T"!c"L#"c#L"_c/__c/__!}
^ _~
 ~A(T_4(x)=4*x^2*(2*x*x-1)-4*x*x+1)~p0
5 ~sb/_!!   }
#/!  c#T"!c"L# c"H#"c"L" c"H#"c#L"_c/__c/__!}
#/!  c#T"!c"L# c"H#"c"L"!c"T! c#L"_c/__c/__!}
^ _~
 ~A(T_6(x))~p1
0 ~A(T_6(x)=32*x^6-48*x^4+18*x^2-1)~p0
255 ~sb/_!!   }
"&!  c#T"!c"L%_c/__c/__}
^ _~A(T_6(x)=2*x*T_5(x)-~
 T_4(x))~p0
1 ~sb/^!!   }
#'!  c#T"!c#L"_c/__c/__!}
^ _~A(T_6(x)=2*x*(2*x*T_~
 4(x)-T_3(x))-(2*x*T_3(x)-T_2(x)))~p0
2 ~sb/_!!   }
#+!  c#T"!c"L" c"H#"c#L"_c/__c/__!}
#+!  c#T"!c"L"!c"T! c#L"_c/__c/__!}
^ _~
 ~A(T_6(x)=4*x^2*T_4(x)-4*x*T_3(x)+T_2(x))~p0
3 ~sb/_!!   }
"&!  c#T"!c"L"_c/__c/__}
^ _~A(T_6(x)=4*x^2*(2*x*~
 T_3(x)-T_2(x))-4*x*(2*x*T_2(x)-T_1(x))+(2*x*T_1(x)-T_0(x)))~p0
4 ~sb/_!!   }
#+!  c#T"!c"L# c"H#"c#L"_c/__c/__!}
#-!  c#T"!c"L#!c"T! c"H#"c#L"_c/__c/__!}
#)!  c#T"!c"L#"c#L"_c/__c/__!}
^ _~
 ~A(T_6(x)=8*x^3*T_3(x)-12*x^2*T_2(x)+6*x*T_1(x)-T_0(x))~p0
5 ~sb/_!!   }
"&!  c#T"!c"L#_c/__c/__}
^ _~A(T_6(x)=8*x^3*(2*x*~
 T_2(x)-T_1(x))-12*x^2*(2*x*T_1(x)-T_0(x))+6*x*x-1)~p0
6 ~sb/_!!   }
#+!  c#T"!c"L$ c"H#"c#L"_c/__c/__!}
#-!  c#T"!c"L$!c"T! c"H#"c#L"_c/__c/__!}
#+!  c#T"!c"L$"c"H#"c#L"_c/__c/__!}
#+!  c#T"!c"L$#c"T! c#L"_c/__c/__!}
^ _~
 ~A(T_6(x)=16*x^4*T_2(x)-32*x^3*T_1(x)+12*x^2*T_0(x)+6*x^2-1)~p0
7 ~sb/_!!   }
"&!  c#T"!c"L$_c/__c/__}
^ _~A(T_6(x)=16*x^4*(2*x*~
 T_1(x)-T_0(x))-32*x^3*x+12*x^2*1+6*x^2-1)~p0
8 ~sb/_!!   }
#+!  c#T"!c"L% c"H#"c#L"_c/__c/__!}
#-!  c#T"!c"L%!c"T! c"H#"c#L"_c/__c/__!}
#+!  c#T"!c"L%"c"H#"c#L"_c/__c/__!}
^ _~
 ~A(T_6(x)=16*x^4*(2*x*x-1)-32*x^3*x+12*x^2*1+6*x^2-1)~p0
9 ~sb/_!!   }
#/!  c#T"!c"L% c"H#"c"L" c"H#"c#L"_c/__c/__!}
#/!  c#T"!c"L% c"H#"c"L"!c"T! c#L"_c/__c/__!}
^ _~t~p0
1 ~c1
3 14 -1 8 14 -1 ~c2
4 14 -1 2 14 -1 1 14 -1 ~c2
5 14 -1 4 14 -1 1 14 -1 ~c1
6 14 -1 5 14 -1 ~c2
7 14 -1 6 14 -1 1 14 -1 ~c2
8 14 -1 7 14 -1 1 14 -1 ~c1
10 14 -1 19 14 -1 ~c2
11 14 -1 9 14 -1 1 14 -1 ~c2
12 14 -1 11 14 -1 1 14 -1 ~c1
13 14 -1 12 14 -1 ~c2
14 14 -1 13 14 -1 1 14 -1 ~c1
15 14 -1 14 14 -1 ~c2
16 14 -1 15 14 -1 1 14 -1 ~c1
17 14 -1 16 14 -1 ~c2
18 14 -1 17 14 -1 1 14 -1 ~c2
19 14 -1 18 14 -1 1 14 -1 ~e