tchebyshev1 takes as argument an integer n and optionnally a
variable name (by default x).
tchebyshev1 returns the Tchebychev polynomial of first kind
of degree n.
The Tchebychev polynomial of first kind T(n,x) is defined by
T(n,x)= cos(n.arccos(x)) |
and verify 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
<f,g>= | ∫ |
|
| dx |
Input :
Output :
^
4+-8*x^
2+1Input :
Output :
^
4+-8*y^
2+1Indeed
|