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The Maxima on-line user's manual

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Chebyshev_t

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

H_oper(f):= diff(diff(f, x), x) - (x*x+1) * f;
-integrate(chebyshev_t(2,x) * H_oper(chebyshev_t(0,x)) * w, x, -1, 1);

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

(%o1)                                true
(%i2) 

Related Examples

chebyshev_t-do-mod

/* input numbers k an...

n:248;

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

Calculate

chebyshev_t-do

/* b=0,6 (mod 8) , n&...

n:31;

a:6;

Calculate

chebyshev_t

chebyshev_t(2,x);

Calculate

chebyshev_t-do-mod

/* input numbers k an...

n:23;

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

Calculate

chebyshev_t-do-mod

/* input numbers k an...

n:4;

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

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chebyshev_t-do

/* b=0,2 (mod 8) , n&...

n:347;

a:6;

Calculate

chebyshev_t-do-mod

/* input numbers k an...

n:556;

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

Calculate

chebyshev_t-do-mod

/* input numbers k an...

n:27;

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

Calculate

chebyshev_t-expand-horner

g(x):= 2.0* chebyshev...

horner(g(x), x);

expand(g(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,T6(x),p(x),q(x)]);

ratsimp((chebyshev_t(...

x^6;

ratsimp((chebyshev_t(...

Calculate