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An inequality from the handbook of mathematical functions (by Abramowitz and Stegun)

score 1.6k · Answer 1 · 2026-04-11 09:30:02

1.6k

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An inequality from the handbook of mathematical functions (by Abramowitz and Stegun)

Published on 11 Apr 2026 - 9:30

score 141 · Answer 2 · 2026-04-12 12:20:18

141

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How to prove the first inequality?

Published on 12 Apr 2026 - 12:20

score 630 · Answer 3 · 2026-04-13 23:38:00

630

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When is Hardy's inequality a strict inequality?

Published on 13 Apr 2026 - 23:38

score 239 · Answer 4 · 2026-04-14 21:52:44

239

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Prove that $\int_0^1f(x)dx$$\int_0^1g(x)dx\ge1$.

Published on 14 Apr 2026 - 21:52

score 822 · Answer 5 · 2026-04-14 19:52:47

822

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Do inequalities that hold for infinite sums hold for integrals too?

Published on 14 Apr 2026 - 19:52

score 395 · Answer 6 · 2026-04-14 10:39:31

395

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A variation of Jensens inequality .

Published on 14 Apr 2026 - 10:39

score 2.1k · Answer 7 · 2026-04-16 20:53:03

2.1k

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Prove the following integral inequality: $\int_{0}^{1}f(g(x))dx\le\int_{0}^{1}f(x)dx+\int_{0}^{1}g(x)dx$

Published on 16 Apr 2026 - 20:53

score 581 · Answer 8 · 2026-04-12 05:26:15

581

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integration inequality

Published on 12 Apr 2026 - 5:26

score 192 · Answer 9 · 2026-04-10 10:23:35

192

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Inequalities of integrals of periodic functions

Published on 10 Apr 2026 - 10:23

score 158 · Answer 10 · 2026-04-11 17:17:19

158

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How to asymptotically estimate a lower bound of this function?

Published on 11 Apr 2026 - 17:17

score 255 · Answer 11 · 2026-04-17 06:34:55

255

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Given $\int_0^1 x f(x)dx=0$, show that $\int_0^1|1-f(x)|dx>1/2$

Published on 17 Apr 2026 - 6:34

score 2.1k · Answer 12 · 2026-05-16 23:21:10

2.1k

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Holder's inequality for infinite products

Published on 16 May 2026 - 23:21

score 141 · Answer 13 · 2026-04-17 11:46:15

141

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Need to prove $\frac{3}{5}(2^{\frac{1}{3}}-1)\le\int_0^1\frac{x^4}{(1+x^6)^{\frac{2}{3}}}dx\le1$

Published on 17 Apr 2026 - 11:46

score 431 · Answer 14 · 2026-04-16 21:46:13

431

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$3\int_{0}^{1}(f'(x))^2dx \geq (2\int_{0}^{1}f(x)dx)^2 \impliedby 2\int_{0}^{\frac{1}{2}}f(x)\,\mathrm dx=\int_{\frac{1}{2}}^{1}f(x) \,\mathrm dx$

Published on 16 Apr 2026 - 21:46

score 250 · Answer 15 · 2026-04-17 06:04:15

250

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integer Random Walk with step size governed by a distribution.

Published on 17 Apr 2026 - 6:04

List Question

An inequality from the handbook of mathematical functions (by Abramowitz and Stegun)

How to prove the first inequality?

When is Hardy's inequality a strict inequality?

Prove that $\int_0^1f(x)dx$$\int_0^1g(x)dx\ge1$.

Do inequalities that hold for infinite sums hold for integrals too?

A variation of Jensens inequality .

Prove the following integral inequality: $\int_{0}^{1}f(g(x))dx\le\int_{0}^{1}f(x)dx+\int_{0}^{1}g(x)dx$

integration inequality

Inequalities of integrals of periodic functions

How to asymptotically estimate a lower bound of this function?

Given $\int_0^1 x f(x)dx=0$, show that $\int_0^1|1-f(x)|dx>1/2$

Holder's inequality for infinite products

Need to prove $\frac{3}{5}(2^{\frac{1}{3}}-1)\le\int_0^1\frac{x^4}{(1+x^6)^{\frac{2}{3}}}dx\le1$

$3\int_{0}^{1}(f'(x))^2dx \geq (2\int_{0}^{1}f(x)dx)^2 \impliedby 2\int_{0}^{\frac{1}{2}}f(x)\,\mathrm dx=\int_{\frac{1}{2}}^{1}f(x) \,\mathrm dx$

integer Random Walk with step size governed by a distribution.

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