 
 
 
11.4.4  Chebyshev polynomials of the first kind
The Chebyshev polynomial of first kind T(n,x) is defined by
and satisfy the recurrence relation:
| T(0,x)=1,    T(1,x)=x,    T(n,x)=2xT(n−1,x)−T(n−2,x). | 
The polynomials T(n,x) are orthogonal for the scalar product
The tchebyshev1
command finds the Chebyshev polynomials of
the first kind.
- 
tchebyshev1 takes one mandatory argument and one
optional argument:
- 
n, an integer.
- Optionally x, a variable name (by default x).
 
- tchebyshev1(n  ⟨,x⟩) returns
the Chebyshev polynomial of first kind of degree n.
Examples
Indeed, cos(4x)=Re((cosx+i sinx)4)=cos4 x−6cos2 x (1−cos2 x)+((1−cos2 x))2=T(4,cos(x)).
 
 
