Explore: Chebyshev Series

The Chebyshev polynomials are two sequences of orthogonal polynomials related to the cosine and sine functions, notated as T n ( x ) {\displaystyle T_{n}(x)}

Pafnuty Lvovich Chebyshev (Russian: Пафну́тий Льво́вич Чебышёв, IPA: [pɐfˈnutʲɪj ˈlʲvovʲɪtɕ tɕɪbɨˈʂof]) (16 May [O.S. 4 May] 1821 – 8 December [O.S. 26

summation, is a recursive method to evaluate a linear combination of Chebyshev polynomials. The method was published by Charles William Clenshaw in 1955

Chebyshev filters are analog or digital filters that have a steeper roll-off than Butterworth filters, and have either passband ripple (type I) or stopband

OEIS: A200138 psi(1/5) to psi(4/5). Implementation in the GNU Scientific library C function with the Chebyshev series Java implementation with Taylor series

In probability theory, Chebyshev's inequality (also called the Bienaymé–Chebyshev inequality) provides an upper bound on the probability of deviation of

the Taylor series expansion are often convenient for theoretical work but less useful for practical applications. Truncated Chebyshev series, however,

Regressive discrete Fourier series, in which the period is determined by the data rather than fixed in advance. Discrete Chebyshev transforms (on the 'roots'

available. The (truncated) series can be used to compute function values numerically, (often by recasting the polynomial into the Chebyshev form and evaluating

r/R\equiv \sin \theta ,\quad 1-(r/R)^{2}=\cos ^{2}\theta ,} the Fourier-Chebyshev series coefficients g emerge as f ( r ) ≡ r m ∑ j g m , j cos ⁡ ( j θ ) =