List questions from harmonic-numbers

Published on 13 Oct 2014 - 3:05

141

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Two alternating Euler sums

Published on 25 Mar 2026 - 2:56

1.6k

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What is a closed form for ${\large\int}_0^1\frac{\ln^3(1+x)\,\ln^2x}xdx$?

Published on 26 Mar 2026 - 2:45

140

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On limits related to $\frac1{\ln n}\sum\limits_{r=1}^{n^4}\frac1r$ when $n\to\infty$

Published on 16 Oct 2014 - 7:13

1.1k

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Harmonic numbers, proof that h2^k >= 1+(k/2) with induction

Published on 17 Oct 2014 - 18:30

299

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Asymptotic behavior of $\sum\limits_{k=1}^n \frac{1}{k^{\alpha}}$ for $\alpha > \frac{1}{2}$

Published on 24 Oct 2014 - 6:25

1.1k

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Harmonic number identity

Published on 25 Mar 2026 - 21:00

939

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Closed form of $\sum_{n=1}^{\infty} \left(\frac{H_n}{n}\right)^4$

Published on 27 Oct 2014 - 21:35

745

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Using induction to prove an equality in harmonic numbers

Published on 28 Oct 2014 - 3:38

2.9k

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Prove that the sum of harmonic series 1..n can be expressed as (n+1)H_n -n

Published on 05 Nov 2014 - 3:03

44

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A question related to harmonic numbers

Published on 11 Nov 2014 - 19:41

1.7k

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Sum of Harmonic numbers $\sum\limits_{n=1}^{\infty} \frac{H_n^{(2)}}{2^nn^2}$

Published on 15 Nov 2014 - 16:07

1k

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Find the closed form of $\sum_{k=1}^{\infty} \sum_{n=1}^{\infty} \frac{H_n}{kn (k+n)^3}$

Published on 15 Nov 2014 - 21:29

112

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Large-z limit of the other second derivative of the Laguerre polynomial

Published on 20 Nov 2014 - 9:32

2.9k

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How to evaluate $\int_0^1 (\arctan x)^2 \ln(\frac{1+x^2}{2x^2}) dx$

Published on 21 Nov 2014 - 15:08

List Question

Generalized harmonic identity

Two alternating Euler sums

What is a closed form for ${\large\int}_0^1\frac{\ln^3(1+x)\,\ln^2x}xdx$?

On limits related to $\frac1{\ln n}\sum\limits_{r=1}^{n^4}\frac1r$ when $n\to\infty$

Harmonic numbers, proof that h2^k >= 1+(k/2) with induction

Asymptotic behavior of $\sum\limits_{k=1}^n \frac{1}{k^{\alpha}}$ for $\alpha > \frac{1}{2}$

Harmonic number identity

Closed form of $\sum_{n=1}^{\infty} \left(\frac{H_n}{n}\right)^4$

Using induction to prove an equality in harmonic numbers

Prove that the sum of harmonic series 1..n can be expressed as (n+1)H_n -n

A question related to harmonic numbers

Sum of Harmonic numbers $\sum\limits_{n=1}^{\infty} \frac{H_n^{(2)}}{2^nn^2}$

Find the closed form of $\sum_{k=1}^{\infty} \sum_{n=1}^{\infty} \frac{H_n}{kn (k+n)^3}$

Large-z limit of the other second derivative of the Laguerre polynomial

How to evaluate $\int_0^1 (\arctan x)^2 \ln(\frac{1+x^2}{2x^2}) dx$

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