Question

$\lim_{n\to\infty}\left(\sum_{k=0}^{n-1}(\zeta(2)-H_{k,2})-H_n\right)=1$

score 83 · Answer 1 · 2018-11-17 22:05:42

83

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$\lim_{n\to\infty}\left(\sum_{k=0}^{n-1}(\zeta(2)-H_{k,2})-H_n\right)=1$

Published on 17 Nov 2018 - 22:05

score 108 · Answer 2 · 2026-03-25 01:30:05

108

Views

What is this generalization of the Chebyshev polynomials?

Published on 25 Mar 2026 - 1:30

score 76 · Answer 3 · 2018-11-18 12:51:41

76

Views

Prove or disprove: $\frac12-\frac{\psi _2^{(1)}(n+2)}{\log 4}$ have infinite zeros

Published on 18 Nov 2018 - 12:51

score 227 · Answer 4 · 2018-11-18 21:30:32

227

Views

The roots of Bessel functions

Published on 18 Nov 2018 - 21:30

score 163 · Answer 5 · 2018-11-22 21:23:23

163

Views

Show that exp(x) is of the form $e^x$?

Published on 22 Nov 2018 - 21:23

score 58 · Answer 6 · 2018-11-25 05:52:52

58

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finding $\int \frac{(1-x^2)^{n-1}}{(1+x^2)^n}\mathrm{d}x$

Published on 25 Nov 2018 - 5:52

score 142 · Answer 7 · 2026-03-25 01:20:26

142

Views

What is the value of this expression involving the dilogarithm $\operatorname{Li}_2$ and $\sqrt{2}$?

Published on 25 Mar 2026 - 1:20

score 304 · Answer 8 · 2026-03-25 23:52:23

304

Views

Value of the J Invariant at $\frac{1+\sqrt{-163}}{2}$

Published on 25 Mar 2026 - 23:52

score 106 · Answer 9 · 2018-11-26 05:18:33

106

Views

Limiting value of a contour integral

Published on 26 Nov 2018 - 5:18

score 44 · Answer 10 · 2018-11-27 02:32:46

44

Views

Evaluating $\int_{-\infty}^{\infty} xf(x)\delta(x-a) dx$.

Published on 27 Nov 2018 - 2:32

score 67 · Answer 11 · 2018-11-27 23:59:46

67

Views

Do you recognize this infinite series? $\sum_{n=0}^\infty \frac 1{(1+an)^c} \frac{b^n}{n!} $

Published on 27 Nov 2018 - 23:59

score 50 · Answer 12 · 2018-11-28 09:40:12

50

Views

Find a function $f_m $ that enumerates all subsets of $\{1,..,n\}$ of cardinality $m$ in ascending order

Published on 28 Nov 2018 - 9:40

score 63 · Answer 13 · 2026-03-26 13:30:36

63

Views

Proof that β-function ∈ C^∞

Published on 26 Mar 2026 - 13:30

score 258 · Answer 14 · 2018-12-01 04:29:55

258

Views

On $\int_0^{2\pi}e^{\cos2x}\cos(\sin2x)\ \mathrm{d}x=2\pi$

Published on 01 Dec 2018 - 4:29

score 296 · Answer 15 · 2026-03-27 07:17:18

296

Views

Prove that $\sum_{n=0}^{\infty}\frac{\Gamma^2(n+1)}{\Gamma(2n+2)}=\frac{2\pi}{3^{3/2}}$

Published on 27 Mar 2026 - 7:17

List Question

$\lim_{n\to\infty}\left(\sum_{k=0}^{n-1}(\zeta(2)-H_{k,2})-H_n\right)=1$

What is this generalization of the Chebyshev polynomials?

Prove or disprove: $\frac12-\frac{\psi _2^{(1)}(n+2)}{\log 4}$ have infinite zeros

The roots of Bessel functions

Show that exp(x) is of the form $e^x$?

finding $\int \frac{(1-x^2)^{n-1}}{(1+x^2)^n}\mathrm{d}x$

What is the value of this expression involving the dilogarithm $\operatorname{Li}_2$ and $\sqrt{2}$?

Value of the J Invariant at $\frac{1+\sqrt{-163}}{2}$

Limiting value of a contour integral

Evaluating $\int_{-\infty}^{\infty} xf(x)\delta(x-a) dx$.

Do you recognize this infinite series? $\sum_{n=0}^\infty \frac 1{(1+an)^c} \frac{b^n}{n!} $

Find a function $f_m $ that enumerates all subsets of $\{1,..,n\}$ of cardinality $m$ in ascending order

Proof that β-function ∈ C^∞

On $\int_0^{2\pi}e^{\cos2x}\cos(\sin2x)\ \mathrm{d}x=2\pi$

Prove that $\sum_{n=0}^{\infty}\frac{\Gamma^2(n+1)}{\Gamma(2n+2)}=\frac{2\pi}{3^{3/2}}$

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