The Chebyshev polynomials of first kind are defined by the simple formula
It is an example of a trigonometric polynomial.
This can be seen to be a polynomial by expressing as a polynomial of , by using the formula for cosine of angle-sum:
So we have
These polynomials obey the recurrence relation:
which can similarly be seen to be polynomials through either a similar process as the above or by the relation .
The first few are:
The same recurrence relation also holds for :
|Date of creation||2013-03-22 12:22:56|
|Last modified on||2013-03-22 12:22:56|
|Last modified by||drini (3)|
|Defines||Chebyshev polynomial of first kind|
|Defines||Chebyshev polynomial of second kind|