Calculates the Chebyshev polynomial of order n at the point x. Details
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x is any real number. |
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n is the nonnegative order (integer) of the Chebyshev polynomial. |
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T(n,x) is the value of the nth Chebyshev polynomial at the point x. |
The Chebyshev polynomial, Tn(x), is defined by
Tn(x) = cos(n arccos(x))
for n=0, 1, 2, ... and real numbers x.
![]() | Note The result of this definition does not look like a polynomial at first glance, but you can use trigonometric rules to show that ![]() |
These functions form the base of the so called Chebyshev approximation. For
it is
All form an orthogonal system over the weight function
The following diagram shows the first four Chebyshev polynomials of degrees 0, 1, 2, and 3.