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In mathematics the Chebyshev rational functions are a sequence of functions which are both rational and orthogonal. A rational Chebyshev function of degree n is defined as:
Many properties can be derived from the properties of the Chebyshev polynomials of the first kind. Other properties are unique to the functions themselves.
Recursion
Differential equations
Orthogonality
Defining:
The orthogonality of the Chebyshev rational functions may be written:
where equals 2 for n=0 and equals 1 for and is the Kronecker delta function.
Expansion of an arbitrary function
For an arbitrary function the orthogonality relationship can be used to expand :