Question

What is the asymptotic upper bound of a variable in the functional equation $f(x)=\left\lceil\frac{f(x+1)}{\lceil\log_2(f(x+1))\rceil}\right\rceil$?

score 229 · Answer 1 · 2026-03-19 23:51:30

229

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What is the asymptotic upper bound of a variable in the functional equation $f(x)=\left\lceil\frac{f(x+1)}{\lceil\log_2(f(x+1))\rceil}\right\rceil$?

Published on 19 Mar 2026 - 23:51

score 64 · Answer 2 · 2026-03-26 03:11:17

64

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How to find the partial sum when a series uses $\operatorname{ceil}$?

Published on 26 Mar 2026 - 3:11

score 441 · Answer 3 · 2019-02-05 03:18:40

441

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Inverse function of $x-\lfloor x \rfloor $ and $(x-\lfloor x \rfloor)^2$

Published on 05 Feb 2019 - 3:18

score 190 · Answer 4 · 2019-02-05 23:33:25

190

Views

Express $\sum_{a=1}^{p-1} \lfloor{(v+qa)/p}\rfloor$ in closed form.

Published on 05 Feb 2019 - 23:33

score 105 · Answer 5 · 2019-02-08 14:43:31

105

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Rigorous or not?

Published on 08 Feb 2019 - 14:43

score 48 · Answer 6 · 2019-02-12 07:25:35

48

Views

Prove/disprove that $\lfloor x\rfloor \leq t \iff x\leq\lfloor t\rfloor +1$

Published on 12 Feb 2019 - 7:25

score 41 · Answer 7 · 2026-03-26 04:51:08

41

Views

How do I find $E\lfloor X \rfloor$ when $X \sim \text{exp}(2)$?

Published on 26 Mar 2026 - 4:51

score 82 · Answer 8 · 2019-02-12 08:40:36

82

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Why $ \int_{0}^{\infty} \lfloor x \rfloor x dx= \sum_{0}^{\infty}n\int_{n}^{n+1}xdx $

Published on 12 Feb 2019 - 8:40

score 168 · Answer 9 · 2026-03-25 09:29:15

168

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Finding $\lim\limits_{x\to 0} \frac{\lfloor x \rfloor}{x}$ and the different definitions of fractional part function.

Published on 25 Mar 2026 - 9:29

score 185 · Answer 10 · 2019-02-13 14:28:41

185

Views

Find out the value of the integral $\int_{-2}^{2} \lfloor x^2-1\rfloor dx$

Published on 13 Feb 2019 - 14:28

score 81 · Answer 11 · 2019-02-15 01:20:21

81

Views

Integral $\int_{-3}^2 \frac{[x]}{[x]^2+2[x]+x^3}dx$

Published on 15 Feb 2019 - 1:20

score 223 · Answer 12 · 2019-02-15 18:41:51

223

Views

Finite double sum $\sum_{k=0}^N\sum_{l=0}^M\left\lfloor\frac{k+l}{c}\right\rfloor$; any advanced summation technique?

Published on 15 Feb 2019 - 18:41

score 177 · Answer 13 · 2019-02-16 15:40:54

177

Views

Find the difference of ceiling functions

Published on 16 Feb 2019 - 15:40

score 316 · Answer 14 · 2019-02-19 16:21:55

Find all $n$ $\in$ $\Bbb Z^+$ such that: $\lfloor\frac{n}{2}\rfloor \cdot \lfloor \frac{n}{3} \rfloor \cdot \lfloor \frac{n}{4} \rfloor = n^2$

score 102 · Answer 15 · 2019-02-24 17:07:40

102

Views

Prove $\lfloor x + n \rfloor= \lfloor x\rfloor + n : n \in \mathbb{Z}$

Published on 24 Feb 2019 - 17:07

List Question

What is the asymptotic upper bound of a variable in the functional equation $f(x)=\left\lceil\frac{f(x+1)}{\lceil\log_2(f(x+1))\rceil}\right\rceil$?

How to find the partial sum when a series uses $\operatorname{ceil}$?

Inverse function of $x-\lfloor x \rfloor $ and $(x-\lfloor x \rfloor)^2$

Express $\sum_{a=1}^{p-1} \lfloor{(v+qa)/p}\rfloor$ in closed form.

Rigorous or not?

Prove/disprove that $\lfloor x\rfloor \leq t \iff x\leq\lfloor t\rfloor +1$

How do I find $E\lfloor X \rfloor$ when $X \sim \text{exp}(2)$?

Why $ \int_{0}^{\infty} \lfloor x \rfloor x dx= \sum_{0}^{\infty}n\int_{n}^{n+1}xdx $

Finding $\lim\limits_{x\to 0} \frac{\lfloor x \rfloor}{x}$ and the different definitions of fractional part function.

Find out the value of the integral $\int_{-2}^{2} \lfloor x^2-1\rfloor dx$

Integral $\int_{-3}^2 \frac{[x]}{[x]^2+2[x]+x^3}dx$

Finite double sum $\sum_{k=0}^N\sum_{l=0}^M\left\lfloor\frac{k+l}{c}\right\rfloor$; any advanced summation technique?

Find the difference of ceiling functions

Find all $n$ $\in$ $\Bbb Z^+$ such that: $\lfloor\frac{n}{2}\rfloor \cdot \lfloor \frac{n}{3} \rfloor \cdot \lfloor \frac{n}{4} \rfloor = n^2$

Prove $\lfloor x + n \rfloor= \lfloor x\rfloor + n : n \in \mathbb{Z}$

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