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Chebyshev polynomials of the first kind are a set of orthogonal polynomials defined as the solutions to the Chebyshev differential equation and denoted
.
They are used as an approximation to a least squares fit,
and are a special case of the ultra-spherical polynomial (Gegenbauer polynomial)
with .
Chebyshev polynomial of the first kind, can be defined by the contour integral
The first seven Chebyshev polynomials of the first kind are:
Orthogonality
The Chebyshev polynomials are orthogonal polynomials with respect to the weighting function
such that
where is the Kronecker delta.
Applications in statistical mechanics
See also