Question

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

score 646 · Answer 1 · 2019-12-04 19:21:36

646

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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 04 Dec 2019 - 19:21

score 25 · Answer 2 · 2019-12-11 16:39:22

25

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Markov or Chebyshev used Inequality here? stat

Published on 11 Dec 2019 - 16:39

score 293 · Answer 3 · 2019-12-21 13:36:57

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 289 · Answer 4 · 2020-01-06 19:41:45

289

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Chebyshev polynomial generalization for non-integer degrees

Published on 06 Jan 2020 - 19:41

score 179 · Answer 5 · 2020-01-16 10:46:13

179

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

Published on 16 Jan 2020 - 10:46

score 250 · Answer 6 · 2020-02-06 14:25:21

250

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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 06 Feb 2020 - 14:25

score 76 · Answer 7 · 2020-02-28 05:12:13

76

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One of Chebyshev's inequalities

Published on 28 Feb 2020 - 5:12

score 183 · Answer 8 · 2020-02-29 19:05:56

183

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Chebyshev first and second kind recurrence

Published on 29 Feb 2020 - 19:05

score 73 · Answer 9 · 2020-03-14 18:28:33

73

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Square roots modulo p

Published on 14 Mar 2020 - 18:28

score 121 · Answer 10 · 2020-03-19 13:06:27

121

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Chebyshev Polynomials of the first kind

Published on 19 Mar 2020 - 13:06

score 1.1k · Answer 11 · 2020-03-23 21:50:58

1.1k

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Extrema of Chebyshev polynomials (of the first kind)

Published on 23 Mar 2020 - 21:50

score 263 · Answer 12 · 2020-03-25 20:38:01

263

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Extremal property of Chebyshev polynomials of second kind

Published on 25 Mar 2020 - 20:38

score 531 · Answer 13 · 2020-03-26 15:30:09

531

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

Published on 26 Mar 2020 - 15:30

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 281 · Answer 15 · 2020-03-27 23:48:50

281

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Gauss-Chebyshev quadrature formula

Published on 27 Mar 2020 - 23:48

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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