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Chebyshev Polynomials

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The Chebyshev polynomial of degree  is denoted . It is defined as:

 

 

Chebyshev polynomials satisfy the following relationships and recursion formulae:

 

Recursion formulae:

 

 

Zeros, exactly  distinct zeros in the interval , as follows:

 

 

Extrema, exactly  real extrema in the interval , as follows:

 

 

Orthogonality:

 

 


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