Question

Series involving a Logarithm

score 70 · Answer 1 · 2026-03-28 16:14:33

70

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Series involving a Logarithm

Published on 28 Mar 2026 - 16:14

score 1.8k · Answer 2 · 2026-03-26 14:21:15

1.8k

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Find the closed form of $\sum_{n=1}^{\infty} \frac{H_{ n}}{2^nn^4}$

Published on 26 Mar 2026 - 14:21

score 1.1k · Answer 3 · 2014-09-24 22:23:44

1.1k

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How to calculate convolution of two logarithmic function, i.e. $\int \ln(\tau)\ln{(x-\tau)}d\tau$

Published on 24 Sep 2014 - 22:23

score 746 · Answer 4 · 2026-03-26 07:35:33

746

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A problem of Ramanujan's interest: closed form of $1 + 2\sum_{n=1}^{\infty} \frac{\cosh(n\theta)}{\cosh(n\pi)} $

Published on 26 Mar 2026 - 7:35

score 123 · Answer 5 · 2014-09-26 10:05:42

123

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Solving equation involving binomial function

Published on 26 Sep 2014 - 10:05

score 343 · Answer 6 · 2014-09-26 10:56:01

343

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Integrals $\int \frac{1}{\operatorname{arctanh}(x)} \, dx$ and $\int \frac{1}{\operatorname{arccoth}(x)} \, dx$

Published on 26 Sep 2014 - 10:56

score 86 · Answer 7 · 2014-09-26 19:33:16

86

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Antisymmetric asymptotic curve with only simple binary arithmetic?

Published on 26 Sep 2014 - 19:33

score 353 · Answer 8 · 2026-03-25 19:05:51

353

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How to evaluate the following infinite sum involving the Riemann zeta function?

Published on 25 Mar 2026 - 19:05

score 122 · Answer 9 · 2014-09-27 11:48:43

122

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Find $a_{n}$ from a convolution formula

Published on 27 Sep 2014 - 11:48

score 73 · Answer 10 · 2014-09-28 04:08:21

73

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Yet another sum involving binomial coefficients.

Published on 28 Sep 2014 - 4:08

score 193 · Answer 11 · 2026-03-26 04:52:03

193

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Finding a formula for the sums $2^0 + 2^1 + 2^2 + 2^3 + \cdots + 2^n$

Published on 26 Mar 2026 - 4:52

score 2.3k · Answer 12 · 2014-09-29 07:08:03

2.3k

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How to compute $\int_{-\infty}^\infty\exp\left(-\frac{(x^2-13x-1)^2}{611x^2}\right)\ dx$

Published on 29 Sep 2014 - 7:08

score 568 · Answer 13 · 2014-09-29 20:34:40

568

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Integral ${\large\int}_0^1\left(-\frac{\operatorname{li} x}x\right)^adx$

Published on 29 Sep 2014 - 20:34

score 206 · Answer 14 · 2026-03-25 11:16:18

206

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Infinite product: $(1-0.5^2)(1-0.5^3)(1-0.5^4)...$

Published on 25 Mar 2026 - 11:16

score 343 · Answer 15 · 2014-10-01 15:45:18

343

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Closed-form for $\sum _{k=4}^{\infty }{\frac { \left( -\ln \left( 2 \right) \right) ^ {k}\zeta \left( 4-k \right) }{k!}}$

Published on 01 Oct 2014 - 15:45

List Question

Series involving a Logarithm

Find the closed form of $\sum_{n=1}^{\infty} \frac{H_{ n}}{2^nn^4}$

How to calculate convolution of two logarithmic function, i.e. $\int \ln(\tau)\ln{(x-\tau)}d\tau$

A problem of Ramanujan's interest: closed form of $1 + 2\sum_{n=1}^{\infty} \frac{\cosh(n\theta)}{\cosh(n\pi)} $

Solving equation involving binomial function

Integrals $\int \frac{1}{\operatorname{arctanh}(x)} \, dx$ and $\int \frac{1}{\operatorname{arccoth}(x)} \, dx$

Antisymmetric asymptotic curve with only simple binary arithmetic?

How to evaluate the following infinite sum involving the Riemann zeta function?

Find $a_{n}$ from a convolution formula

Yet another sum involving binomial coefficients.

Finding a formula for the sums $2^0 + 2^1 + 2^2 + 2^3 + \cdots + 2^n$

How to compute $\int_{-\infty}^\infty\exp\left(-\frac{(x^2-13x-1)^2}{611x^2}\right)\ dx$

Integral ${\large\int}_0^1\left(-\frac{\operatorname{li} x}x\right)^adx$

Infinite product: $(1-0.5^2)(1-0.5^3)(1-0.5^4)...$

Closed-form for $\sum _{k=4}^{\infty }{\frac { \left( -\ln \left( 2 \right) \right) ^ {k}\zeta \left( 4-k \right) }{k!}}$

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