Sponsored links: Algebra eBooks
 

Help Index

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

The Maxima on-line user's manual

Algebra Calculator

Search:

Chebyshev_t

Function: chebyshev_t (<n>, <x>) The Chebyshev function of the first kind.

u : exp((x^2 - 1)/2);
a : -1;
b : 1;
w : 1 / sqrt(1 - x * x);
N : 4;
H_oper(f):= diff(diff(f, x), x) - (x*x+1) * f;
h[i,j]:= integrate(chebyshev_t(2*i,x) * H_oper(chebyshev_t(2*j,x)) * w, x, -1, 1);
H : genmatrix(h, N, N);
f[i,j]:= -integrate(chebyshev_t(2*i-1,x) * H_oper(chebyshev_t(0,x)) * w, x, -1, 1);
F : genmatrix(f, N, 1);
c : invert(H) . F;
u_N : chebyshev_t(0,x) + lsum(c[j, 1] * chebyshev_t(2*j-1, x), j, makelist(i, i, 1, N));
E_t : quad_qag(abs(u-u_N), x, a, b, 6)[1];
plot2d([u, u_N], [x, -1,1]);

Reference: Abramowitz and Stegun, equation 22.5.47, page 779.

(%o1)                                true
(%i2) 

Related Examples

chebyshev_t-expand-horner-orthopoly_weight

g(x):= 0.11* chebyshe...

horner(g(x), x);

expand(g(x));

Calculate

chebyshev_t-plot2d
plot2d(chebyshev_t(6,x),[x,-1,1]);

plot2d(chebyshev_t(6,...

Calculate

chebyshev_t

chebyshev_t(2,x);

Calculate

chebyshev_t-plot2d-ratsimp
plot2d([(chebyshev_t(6,x))/2^5,x^6,x^6-(chebyshev_t(6,x))/2^5],[x,-1,1],[y,-0.2,0.2],[legend,Tst,p(x),q(x)]);

ratsimp(chebyshev_t(6...

ratsimp(x^6-(chebyshe...

plot2d([(chebyshev_t(...

Calculate

chebyshev_t-diff-integrate

H_oper(f):= diff(diff...

-integrate(chebyshev_...

Calculate

chebyshev_t-plot2d
plot2d(chebyshev_t(6,x),[x,-1,1]);

plot2d(chebyshev_t(6,...

Calculate

chebyshev_t-do

/* b=4,6 (mod 8) , n&...

n:19;

a:6;

Calculate

chebyshev_t-do-mod

/* input numbers k an...

n:17;

(s:2*chebyshev_t(k,3)...

Calculate

chebyshev_t-do-mod

/* input numbers k an...

n:7;

(s:2*chebyshev_t(k,3)...

Calculate

chebyshev_t-do-mod

/* input numbers k an...

n:248;

(s:2*chebyshev_t(k,3)...

Calculate