Question

Get a good approximation of $\int_0^1 \left(H_x\right)^2 dx$, where $H_x$ is the generalized harmonic number

score 398 · Answer 1 · 2017-03-14 12:20:42

398

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Get a good approximation of $\int_0^1 \left(H_x\right)^2 dx$, where $H_x$ is the generalized harmonic number

Published on 14 Mar 2017 - 12:20

score 106 · Answer 2 · 2017-03-20 02:35:44

106

Views

Is this procedure on Harmonic Series correct?

Published on 20 Mar 2017 - 2:35

score 141 · Answer 3 · 2017-03-22 12:09:11

141

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About the extension of $H_n$ to non-integer arguments

Published on 22 Mar 2017 - 12:09

score 95 · Answer 4 · 2017-03-27 10:51:09

95

Views

What is the integer part of the sum of the reciprocals of the first $2017$ positive integers?

Published on 27 Mar 2017 - 10:51

score 75 · Answer 5 · 2017-03-27 22:01:28

75

Views

How can we one show that $\sum_{i=1}^{\infty}\sum_{j=1}^{2k}(-1)^{j-1}{2\over i+j}=H_k?$

Published on 27 Mar 2017 - 22:01

score 134 · Answer 6 · 2017-03-28 15:26:24

134

Views

Showing that $\sum_{k=0}^{n}(-1)^k{n\choose k}{1\over k+1}\sum_{j=0}^{k}{H_{j+1}\over j+1}={1\over (n+1)^3}$

Published on 28 Mar 2017 - 15:26

score 128 · Answer 7 · 2017-03-30 09:32:38

128

Views

Prove $1 + \frac{n}{2} \leq 1+ \frac{1}{2} +\frac{1}{3} +\cdots + \frac{1}{2^n}$ for all natural numbers $n$

Published on 30 Mar 2017 - 9:32

score 526 · Answer 8 · 2026-03-25 14:25:33

526

Views

What is the closed form of $\sum_{n\geq 1}(-1)^{n-1}\psi'(n)^2$?

Published on 25 Mar 2026 - 14:25

score 60 · Answer 9 · 2026-03-25 13:55:09

60

Views

Harmonic nesting: How often nodes of different sin waves line up with each other?

Published on 25 Mar 2026 - 13:55

score 347 · Answer 10 · 2017-04-02 19:47:55

347

Views

How can one evaluate the basic Tornheim Sum?

Published on 02 Apr 2017 - 19:47

score 70 · Answer 11 · 2017-04-03 18:38:52

70

Views

calculate elements of harmonic floor progression

Published on 03 Apr 2017 - 18:38

score 205 · Answer 12 · 2017-04-05 07:43:21

205

Views

Evaluation of two Euler type sums

Published on 05 Apr 2017 - 7:43

score 166 · Answer 13 · 2017-04-08 00:10:09

166

Views

Divisibility of numerator of harmonic series $H(j)=1+\frac 12+\cdots+\frac 1j$

Published on 08 Apr 2017 - 0:10

score 382 · Answer 14 · 2023-01-30 09:41:38

382

Views

Two nice (challenging) binoharmonic series

Published on 30 Jan 2023 - 9:41

score 229 · Answer 15 · 2023-02-09 13:23:23

229

Views

Non-$\zeta$ term of the sum $\sum\limits_{k = 1}^{\infty} \frac{H_k H_{k+m}}{k^2}$ for $m \in \mathbb{N}_0$

Published on 09 Feb 2023 - 13:23

List Question

Get a good approximation of $\int_0^1 \left(H_x\right)^2 dx$, where $H_x$ is the generalized harmonic number

Is this procedure on Harmonic Series correct?

About the extension of $H_n$ to non-integer arguments

What is the integer part of the sum of the reciprocals of the first $2017$ positive integers?

How can we one show that $\sum_{i=1}^{\infty}\sum_{j=1}^{2k}(-1)^{j-1}{2\over i+j}=H_k?$

Showing that $\sum_{k=0}^{n}(-1)^k{n\choose k}{1\over k+1}\sum_{j=0}^{k}{H_{j+1}\over j+1}={1\over (n+1)^3}$

Prove $1 + \frac{n}{2} \leq 1+ \frac{1}{2} +\frac{1}{3} +\cdots + \frac{1}{2^n}$ for all natural numbers $n$

What is the closed form of $\sum_{n\geq 1}(-1)^{n-1}\psi'(n)^2$?

Harmonic nesting: How often nodes of different sin waves line up with each other?

How can one evaluate the basic Tornheim Sum?

calculate elements of harmonic floor progression

Evaluation of two Euler type sums

Divisibility of numerator of harmonic series $H(j)=1+\frac 12+\cdots+\frac 1j$

Two nice (challenging) binoharmonic series

Non-$\zeta$ term of the sum $\sum\limits_{k = 1}^{\infty} \frac{H_k H_{k+m}}{k^2}$ for $m \in \mathbb{N}_0$

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