List questions from harmonic-numbers

Published on 24 Dec 2021 - 20:21

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A sum similar to Harmonic numbers.

Published on 25 Dec 2021 - 4:14

120

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Evaluating $\sum_{n=0}^\infty\frac{(1/2)_n}{n!}(H_n-H_{n-1/2})$

Published on 26 Mar 2026 - 14:34

109

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Convergence of double integral involving logarithms and binomials? Can anyone present a simpler proof?

Published on 27 Jan 2022 - 14:16

99

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Change in order of integration in an integral

Published on 05 Feb 2022 - 17:57

277

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How do I evaluate the sum $\sum_{n=1,3,5,...}^{\infty} \frac{1}{n^{4}}$?

Published on 20 Feb 2022 - 16:06

1.9k

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Are these generalizations known in the literature?

Published on 28 Mar 2026 - 15:35

116

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Approximation of harmonic numbers and their analytical inverse.

Published on 31 Mar 2026 - 16:16

54

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How this sum can be transformed into a relation with harmonic series?

Published on 20 Mar 2022 - 10:32

276

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Are these two recursive formulas known in the literature?

Published on 06 Apr 2022 - 1:37

493

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Finding $\sum_{n=1}^{\infty}\frac{(-1)^n (H_{2n}-H_{n})}{n2^n \binom{2n}{n}}$

Published on 07 Apr 2022 - 8:32

132

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Closed form for $\sum_{n=2}^{\infty} \big{(}H_{n,n}-1\big{)} $?

Published on 18 Apr 2022 - 20:32

56

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Show that. If $H_{j}=\sum\limits_{k=1}^{j}{\frac{1}{k}}$, than $H_{2^n}\geq 1+\frac{n}{2}$ for all natural numbers.

Published on 21 Apr 2022 - 13:16

64

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why is that $H_{k-1/2}-H_k = 2H_{2k}-H_k$?

Published on 15 May 2022 - 4:14

169

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Question on a closed-form expression related to the harmonic number $H_n$

Published on 18 May 2022 - 22:26

List Question

Approximate $\sum\limits_{k=0}^{m-1}\frac{k}{m-k}$

A sum similar to Harmonic numbers.

Evaluating $\sum_{n=0}^\infty\frac{(1/2)_n}{n!}(H_n-H_{n-1/2})$

Convergence of double integral involving logarithms and binomials? Can anyone present a simpler proof?

Change in order of integration in an integral

How do I evaluate the sum $\sum_{n=1,3,5,...}^{\infty} \frac{1}{n^{4}}$?

Are these generalizations known in the literature?

Approximation of harmonic numbers and their analytical inverse.

How this sum can be transformed into a relation with harmonic series?

Are these two recursive formulas known in the literature?

Finding $\sum_{n=1}^{\infty}\frac{(-1)^n (H_{2n}-H_{n})}{n2^n \binom{2n}{n}}$

Closed form for $\sum_{n=2}^{\infty} \big{(}H_{n,n}-1\big{)} $?

Show that. If $H_{j}=\sum\limits_{k=1}^{j}{\frac{1}{k}}$, than $H_{2^n}\geq 1+\frac{n}{2}$ for all natural numbers.

why is that $H_{k-1/2}-H_k = 2H_{2k}-H_k$?

Question on a closed-form expression related to the harmonic number $H_n$

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