Chebyshev Polynomial Calculator

T_n(x) = cos(n·arccos(x))

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n (degree)

T_6(0.5)

1.000000

U_6(0.5)

1.000000

Sequence at x=0.5

n=0T=1.0000U=1.0000

n=1T=0.5000U=1.0000

n=2T=-0.5000U=0.0000

n=3T=-1.0000U=-1.0000

n=4T=-0.5000U=-1.0000

n=5T=0.5000U=0.0000

n=6T=1.0000U=1.0000

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About Chebyshev Polynomial Calculator

A Chebyshev polynomial calculator computing T_n(x) (first kind) and U_n(x) (second kind) using recurrence T_{n+1}=2xT_n−T_{n-1}. Chebyshev nodes minimize Runge's phenomenon. Used in spectral methods, filters, numerical integration. Client-side.

Chebyshev Polynomial Calculator Features

T_n(x) value
U_n(x) value
Coefficients
Recurrence
Nodes

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