share/orthopoly/test_orthopoly.mac

48   chebyshev_t,
173 foo : makelist(chebyshev_t(n,cos(x)) - cos(n*x),n,0, 3)$
279 cheb_rec(n,m) := 2 * chebyshev_t(m,x) * chebyshev_t(n,x)
280 - chebyshev_t(n+m,x) - chebyshev_t(n-m,x)$
294  - chebyshev_t(n+m,x) + chebyshev_t(n-m,x)$
307 cheb_rec(n,m) := 2*chebyshev_t(m,x) * chebyshev_u(n-1,x)
320 cheb_rec(n,m) := 2*chebyshev_t(n,x) * chebyshev_u(m-1,x)
333 cheb_rec(n) := 2*chebyshev_t(n,x) * chebyshev_u(n-1,x)
478 baz(n) := sum(chebyshev_t(2*k,x) ,k,0,n)  - (1 + chebyshev_u(2*n,x))/2$
486 baz(n) := sum(chebyshev_t(2*k+1,x) ,k,0,n-1)  - chebyshev_u(2*n-1,x)/2$
494 baz(n) := sum(chebyshev_u(2*k,x) ,k,0,n)  - (1-chebyshev_t(2*n+2,x))/(2 * (1-x^2))$
502 baz(n) := sum(chebyshev_u(2*k+1,x) ,k,0,n-1)  - (x-chebyshev_t(2*n+1,x))/(2 * (1-x^2))$
560    p : sum(xargs(chebyshev_t(2*i,x)),i,0,n),
612    p : sum(xargs(chebyshev_t(2*i+1,x)),i,0,n-1),
744 test_name : "random chebyshev_t float"$
749    exact : float(chebyshev_t(n,x)),
750    approx : chebyshev_t(n,float(x)),
752    if (foo = 1) then print("chebyshev_t float error; n = ",n, "x = ",x),
764    if (foo = 1) then print("chebyshev_t float error; n = ",n, "x = ",x),
1098 test_name : "chebyshev_t gradef test"$
1101    foo : diff(chebyshev_t(n,x^2) - chebyshev_t(i,x^2),x),
1259 test_name : "chebyshev_t sum representation"$
1260 foo : chebyshev_t(n,2)$
1262 foo : rat(foo - chebyshev_t(5,2))$
1345 foo : orthopoly_recur(chebyshev_t,[m,x])$
1481 foo : orthopoly_weight(chebyshev_t,[n,x])$
1482 foo : integrate(chebyshev_t(5,x) * chebyshev_t(4,x)
1601 foo : ['(chebyshev_t(1,x)),
1602 '(chebyshev_t(2,x)),
1603 '(chebyshev_t(3,x)),
1604 '(chebyshev_t(4,x)),
1605 '(chebyshev_t(5,x))]$