Question

Classic Complex Numbers - Given $z+\frac 1z=2\cos 3^\circ$, find least integer greater than $z^{2000}+\frac 1{z^{2000}}$

score 647 · Answer 1 · 2026-03-25 12:35:06

647

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Classic Complex Numbers - Given $z+\frac 1z=2\cos 3^\circ$, find least integer greater than $z^{2000}+\frac 1{z^{2000}}$

Published on 25 Mar 2026 - 12:35

score 26 · Answer 2 · 2026-03-25 12:32:40

26

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Markov or Chebyshev used Inequality here? stat

Published on 25 Mar 2026 - 12:32

score 294 · Answer 3 · 2026-03-25 14:25:09

Derive the explicit expression of the Chebyshev polynimial: $T_n(x) =n\sum _{k=0}^{n}(-2)^{k}{\frac {(n+k-1)!}{(n-k)!(2k)!}}(1-x)^{k}$.

score 290 · Answer 4 · 2026-03-25 12:30:32

290

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Chebyshev polynomial generalization for non-integer degrees

Published on 25 Mar 2026 - 12:30

score 180 · Answer 5 · 2026-03-25 12:32:37

180

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Spectrum self-adjoint operator induced by right shift operator on $\ell^2(\mathbb{N})$.

Published on 25 Mar 2026 - 12:32

score 251 · Answer 6 · 2026-03-25 14:25:21

251

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Prove that $\int_1^a \frac{T_n(x) T_n(x/a)}{\sqrt{a^2 - x^2} \sqrt{x^2 - 1^2}} \frac{a}{x} \mathrm{d}x = \frac{\pi}{2}$

Published on 25 Mar 2026 - 14:25

score 78 · Answer 7 · 2026-03-27 09:04:48

78

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One of Chebyshev's inequalities

Published on 27 Mar 2026 - 9:04

score 184 · Answer 8 · 2026-03-25 12:30:37

184

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Chebyshev first and second kind recurrence

Published on 25 Mar 2026 - 12:30

score 74 · Answer 9 · 2026-03-25 12:30:04

74

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Square roots modulo p

Published on 25 Mar 2026 - 12:30

score 122 · Answer 10 · 2026-03-25 12:33:03

122

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Chebyshev Polynomials of the first kind

Published on 25 Mar 2026 - 12:33

score 1.1k · Answer 11 · 2026-03-25 12:34:49

1.1k

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Extrema of Chebyshev polynomials (of the first kind)

Published on 25 Mar 2026 - 12:34

score 264 · Answer 12 · 2026-03-25 12:34:35

264

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Extremal property of Chebyshev polynomials of second kind

Published on 25 Mar 2026 - 12:34

score 532 · Answer 13 · 2026-03-25 12:33:06

532

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Definite integral involving Legendre polynomials with weight function $\sqrt{1-x^2}$

Published on 25 Mar 2026 - 12:33

score 280 · Answer 14 · 2026-03-25 03:07:39

280

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How would one go about computing a Chebyshev-type quadrature problem with general integration limits of [a,b] instead of [-1,1]?

Published on 25 Mar 2026 - 3:07

score 282 · Answer 15 · 2026-03-25 12:33:07

282

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Gauss-Chebyshev quadrature formula

Published on 25 Mar 2026 - 12:33

List Question

Classic Complex Numbers - Given $z+\frac 1z=2\cos 3^\circ$, find least integer greater than $z^{2000}+\frac 1{z^{2000}}$

Markov or Chebyshev used Inequality here? stat

Derive the explicit expression of the Chebyshev polynimial: $T_n(x) =n\sum _{k=0}^{n}(-2)^{k}{\frac {(n+k-1)!}{(n-k)!(2k)!}}(1-x)^{k}$.

Chebyshev polynomial generalization for non-integer degrees

Spectrum self-adjoint operator induced by right shift operator on $\ell^2(\mathbb{N})$.

Prove that $\int_1^a \frac{T_n(x) T_n(x/a)}{\sqrt{a^2 - x^2} \sqrt{x^2 - 1^2}} \frac{a}{x} \mathrm{d}x = \frac{\pi}{2}$

One of Chebyshev's inequalities

Chebyshev first and second kind recurrence

Square roots modulo p

Chebyshev Polynomials of the first kind

Extrema of Chebyshev polynomials (of the first kind)

Extremal property of Chebyshev polynomials of second kind

Definite integral involving Legendre polynomials with weight function $\sqrt{1-x^2}$

How would one go about computing a Chebyshev-type quadrature problem with general integration limits of [a,b] instead of [-1,1]?

Gauss-Chebyshev quadrature formula

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