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Proving that a family of complicated functions is less than one particularly simple function

score 51 · Answer 1 · 2026-03-22 04:38:17

51

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Proving that a family of complicated functions is less than one particularly simple function

Published on 22 Mar 2026 - 4:38

score 191 · Answer 2 · 2026-03-25 07:46:28

191

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Evaluate: $\sum\limits_{n\ge1}\sum\limits_{m\ge0}\sum\limits_{k=0}^{n-1}\frac{y^nm^k(-n)^m\delta_{k+m-n+1}}{(k+m-n+1)!\Gamma(n-k)k!n}$

Published on 25 Mar 2026 - 7:46

score 360 · Answer 3 · 2023-03-10 21:31:41

360

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$f(f(z)) = z , f(\exp(z)) = \exp(f(z)) $?

Published on 10 Mar 2023 - 21:31

score 95 · Answer 4 · 2023-03-31 22:42:08

95

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tetration primitive root $q \mod p$

Published on 31 Mar 2023 - 22:42

score 173 · Answer 5 · 2023-04-06 05:01:45

173

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Do we need a new number system for inverse tetration?

Published on 06 Apr 2023 - 5:01

score 135 · Answer 6 · 2026-03-25 13:59:04

135

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Does the distributive property apply to all hyperoperations higher than multiplication?

Published on 25 Mar 2026 - 13:59

score 98 · Answer 7 · 2026-03-25 12:49:54

98

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Closed form for $H(n,k)=\frac{1}{k!}\sum_{j=0}^\infty H(n-k, j)j^k$ where $H(1,k)=\frac{1}{k!}$

Published on 25 Mar 2026 - 12:49

score 92 · Answer 8 · 2023-04-28 00:38:50

92

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How to find what number raised to its own power is equal to a given number?

Published on 28 Apr 2023 - 0:38

score 97 · Answer 9 · 2026-02-24 05:18:32

97

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Evaluating $\frac{d^n}{dt^n}e^{a(t-e^t)}$ as a single series to extend region of convergence for super root function

Published on 24 Feb 2026 - 5:18

score 91 · Answer 10 · 2023-05-24 23:19:10

91

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Iterating $\tanh(A x)$ and $\lim_{x \to +\infty} \tanh^{[r]}(A x) = C_r$?

Published on 24 May 2023 - 23:19

score 126 · Answer 11 · 2026-03-25 13:56:58

126

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How can the domains of all variables of this hyperoperation function be extended to the entire complex plane?

Published on 25 Mar 2026 - 13:56

score 194 · Answer 12 · 2023-05-29 14:03:43

194

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Are there infinitely many $c$-th perfect powers having a constant congruence speed of $c$?

Published on 29 May 2023 - 14:03

score 78 · Answer 13 · 2023-07-01 18:02:24

78

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Infinite power tower for $x > e^{1/e}$

Published on 01 Jul 2023 - 18:02

score 193 · Answer 14 · 2023-07-12 09:49:16

193

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Modular tetration (power tower) for non-coprime numbers case

Published on 12 Jul 2023 - 9:49

score 95 · Answer 15 · 2023-07-23 23:29:41

95

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Is there a set-theoretic construction of tetration and even higher-order Ackermann functions?

Published on 23 Jul 2023 - 23:29

List Question

Proving that a family of complicated functions is less than one particularly simple function

Evaluate: $\sum\limits_{n\ge1}\sum\limits_{m\ge0}\sum\limits_{k=0}^{n-1}\frac{y^nm^k(-n)^m\delta_{k+m-n+1}}{(k+m-n+1)!\Gamma(n-k)k!n}$

$f(f(z)) = z , f(\exp(z)) = \exp(f(z)) $?

tetration primitive root $q \mod p$

Do we need a new number system for inverse tetration?

Does the distributive property apply to all hyperoperations higher than multiplication?

Closed form for $H(n,k)=\frac{1}{k!}\sum_{j=0}^\infty H(n-k, j)j^k$ where $H(1,k)=\frac{1}{k!}$

How to find what number raised to its own power is equal to a given number?

Evaluating $\frac{d^n}{dt^n}e^{a(t-e^t)}$ as a single series to extend region of convergence for super root function

Iterating $\tanh(A x)$ and $\lim_{x \to +\infty} \tanh^{[r]}(A x) = C_r$?

How can the domains of all variables of this hyperoperation function be extended to the entire complex plane?

Are there infinitely many $c$-th perfect powers having a constant congruence speed of $c$?

Infinite power tower for $x > e^{1/e}$

Modular tetration (power tower) for non-coprime numbers case

Is there a set-theoretic construction of tetration and even higher-order Ackermann functions?

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