Question

Correct my proof about : $x^{x^{x^{x^{x^{x}}}}}$ is convex for $0.25<x<0.27$

score 503 · Answer 1 · 2026-04-16 19:52:16

503

Views

Correct my proof about : $x^{x^{x^{x^{x^{x}}}}}$ is convex for $0.25<x<0.27$

Published on 16 Apr 2026 - 19:52

score 511 · Answer 2 · 2026-04-14 08:57:07

511

Views

Prove or disprove that the function is convex .

Published on 14 Apr 2026 - 8:57

score 223 · Answer 3 · 2026-04-13 17:58:25

223

Views

Solution to the Equation $x^x = 0$.

Published on 13 Apr 2026 - 17:58

score 375 · Answer 4 · 2026-04-13 11:30:56

375

Views

Does $\mathrm{\int W(ln(x))dx}$ have a closed form?

Published on 13 Apr 2026 - 11:30

score 92 · Answer 5 · 2026-04-10 21:47:46

92

Views

Is there any formula to sum the series $\sum_{k=1}^n{2^{k^k}}$

Published on 10 Apr 2026 - 21:47

score 436 · Answer 6 · 2026-04-16 08:36:52

436

Views

Integral form(s) of a general tetration/power tower integral solution: $\sum\limits_{n=0}^\infty \frac{(pn+q)^{rn+s}Γ(An+B,Cn+D)}{Γ(an+b,cn+d)}$

Published on 16 Apr 2026 - 8:36

score 415 · Answer 7 · 2026-04-11 11:15:29

415

Views

Can $\int\limits_0^\infty e^{ix^ x}dx$ be written without a limit?

Published on 11 Apr 2026 - 11:15

score 127 · Answer 8 · 2026-04-13 22:09:23

127

Views

About the inequality $f(-x)<\left(\Gamma(1-x)\right)^{\frac{1}{1-x}}$

Published on 13 Apr 2026 - 22:09

score 201 · Answer 9 · 2026-04-16 23:15:36

201

Views

Could someone explain why $\sum_{\substack{a_1,\ldots,a_n\in\mathbb{N}_0\\a_1+\cdots+a_n=n}}\frac{n!}{a_1!\cdots a_n!}=n^n$?

Published on 16 Apr 2026 - 23:15

score 148 · Answer 10 · 2026-04-17 04:35:49

148

Views

Evaluating negative infinite tetration: $\lim\limits_{n\to-\infty}\,^n x=\lim_{n\to\infty}\underbrace{\log_x\left(…\log_x(0)\right)}_n=\,^{-\infty} x$

Published on 17 Apr 2026 - 4:35

score 123 · Answer 11 · 2026-04-14 06:25:38

123

Views

Examples of closed forms of integrals with a power tower argument using W-Lambert function.

Published on 14 Apr 2026 - 6:25

score 1.6k · Answer 12 · 2026-04-16 19:39:10

1.6k

Views

Is each of $\int_0^\infty\frac{dx}{x^x},\int_0^\infty\frac{dx}{x^{x^{x^x}}},\int_0^\infty\frac{dx}{x^{x^{x^{x^{x^x}}}}},\cdots$ less than $2$?

Published on 16 Apr 2026 - 19:39

score 97 · Answer 13 · 2026-04-16 00:21:16

97

Views

$f(n)=$, for even integer’s $n$, $\lim_{n\to\infty} \int_{0}^{\infty} \frac{e^x}{^nx} dx$

Published on 16 Apr 2026 - 0:21

score 147 · Answer 14 · 2026-05-10 18:45:51

147

Views

Correct my sketch of proof about the convexity of the "natural" power tower on $[1,\infty)$

Published on 10 May 2026 - 18:45

score 44 · Answer 15 · 2026-04-14 12:46:49

44

Views

Digits tower power iterate

Published on 14 Apr 2026 - 12:46

List Question

Correct my proof about : $x^{x^{x^{x^{x^{x}}}}}$ is convex for $0.25<x<0.27$

Prove or disprove that the function is convex .

Solution to the Equation $x^x = 0$.

Does $\mathrm{\int W(ln(x))dx}$ have a closed form?

Is there any formula to sum the series $\sum_{k=1}^n{2^{k^k}}$

Integral form(s) of a general tetration/power tower integral solution: $\sum\limits_{n=0}^\infty \frac{(pn+q)^{rn+s}Γ(An+B,Cn+D)}{Γ(an+b,cn+d)}$

Can $\int\limits_0^\infty e^{ix^ x}dx$ be written without a limit?

About the inequality $f(-x)<\left(\Gamma(1-x)\right)^{\frac{1}{1-x}}$

Could someone explain why $\sum_{\substack{a_1,\ldots,a_n\in\mathbb{N}_0\\a_1+\cdots+a_n=n}}\frac{n!}{a_1!\cdots a_n!}=n^n$?

Evaluating negative infinite tetration: $\lim\limits_{n\to-\infty}\,^n x=\lim_{n\to\infty}\underbrace{\log_x\left(…\log_x(0)\right)}_n=\,^{-\infty} x$

Examples of closed forms of integrals with a power tower argument using W-Lambert function.

Is each of $\int_0^\infty\frac{dx}{x^x},\int_0^\infty\frac{dx}{x^{x^{x^x}}},\int_0^\infty\frac{dx}{x^{x^{x^{x^{x^x}}}}},\cdots$ less than $2$?

$f(n)=$, for even integer’s $n$, $\lim_{n\to\infty} \int_{0}^{\infty} \frac{e^x}{^nx} dx$

Correct my sketch of proof about the convexity of the "natural" power tower on $[1,\infty)$

Digits tower power iterate

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