Question

How to solve the functional equation : $T(n)=(\log n)T(\log n)+n$

score 160 · Answer 1 · 2026-03-25 19:04:13

160

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How to solve the functional equation : $T(n)=(\log n)T(\log n)+n$

Published on 25 Mar 2026 - 19:04

score 252 · Answer 2 · 2013-02-27 07:00:26

252

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Solution(s) to $f(x+f(y))+f(y+f(x))=2f(f(x))f(f(y))$

Published on 27 Feb 2013 - 7:00

score 688 · Answer 3 · 2013-02-27 18:57:12

688

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functional equations for trigonometric functions: $f(x+y)=f(x)f(y)-g(x)g(y)$ and $g(x+y)=f(x)g(y)+g(x)f(y)$

Published on 27 Feb 2013 - 18:57

score 69 · Answer 4 · 2013-03-01 04:25:54

69

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$\frac{f(x_1)}{f(x_2)} = \log(\frac{x_1}{x_2}) \implies f(x)=\;?$

Published on 01 Mar 2013 - 4:25

score 154 · Answer 5 · 2013-03-01 06:16:53

154

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$f(xy)=f(x(1-y)) \forall x,y\in (0,1)$, Find all $f:(0,1)\rightarrow \mathbb{R}$

Published on 01 Mar 2013 - 6:16

score 4k · Answer 6 · 2013-03-02 09:32:14

4k

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Additivity + Measurability $\implies$ Continuity

Published on 02 Mar 2013 - 9:32

score 675 · Answer 7 · 2026-03-30 11:33:55

675

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Sufficient condition for a function to be affine

Published on 30 Mar 2026 - 11:33

score 69 · Answer 8 · 2013-03-07 10:00:53

69

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$f(\vec{x_1}+\vec{x_2})=f(\vec{x_1})f(\vec{x_2})$

Published on 07 Mar 2013 - 10:00

score 867 · Answer 9 · 2013-03-07 17:26:52

867

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The number of non-trivial polynomial solutions of the differential equation $x^3y'(x)=y(x^2)$

Published on 07 Mar 2013 - 17:26

score 185 · Answer 10 · 2013-03-08 22:49:16

185

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Map that satisfies $f(\lambda x) = \lambda f(x)$ but not $f(x+y) = f(x)+f(y)$

Published on 08 Mar 2013 - 22:49

score 4.8k · Answer 11 · 2013-03-09 13:35:16

4.8k

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IMO 1987 - function such that $f(f(n))=n+1987$

Published on 09 Mar 2013 - 13:35

score 331 · Answer 12 · 2013-03-10 06:17:59

$f\left ( x+m \right )\left ( f\left ( x \right )+\sqrt{m+1} \right )=-\left ( m+2 \right ),\forall x\in \mathbb{R},m\in \mathbb{Z^+}$

score 1.3k · Answer 13 · 2013-03-11 20:28:49

1.3k

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Functions $f$ satisfying $ f\circ f(x)=2f(x)-x,\forall x\in\mathbb{R}$.

Published on 11 Mar 2013 - 20:28

score 357 · Answer 14 · 2013-03-12 11:25:17

357

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Functions satisfying $\sum_{n=0}^k(-1)^n\binom{k}{k-n}f^{k-n}(x)=0$.

Published on 12 Mar 2013 - 11:25

score 80 · Answer 15 · 2013-03-12 14:50:05

80

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Math question functions help me?

Published on 12 Mar 2013 - 14:50

List Question

How to solve the functional equation : $T(n)=(\log n)T(\log n)+n$

Solution(s) to $f(x+f(y))+f(y+f(x))=2f(f(x))f(f(y))$

functional equations for trigonometric functions: $f(x+y)=f(x)f(y)-g(x)g(y)$ and $g(x+y)=f(x)g(y)+g(x)f(y)$

$\frac{f(x_1)}{f(x_2)} = \log(\frac{x_1}{x_2}) \implies f(x)=\;?$

$f(xy)=f(x(1-y)) \forall x,y\in (0,1)$, Find all $f:(0,1)\rightarrow \mathbb{R}$

Additivity + Measurability $\implies$ Continuity

Sufficient condition for a function to be affine

$f(\vec{x_1}+\vec{x_2})=f(\vec{x_1})f(\vec{x_2})$

The number of non-trivial polynomial solutions of the differential equation $x^3y'(x)=y(x^2)$

Map that satisfies $f(\lambda x) = \lambda f(x)$ but not $f(x+y) = f(x)+f(y)$

IMO 1987 - function such that $f(f(n))=n+1987$

$f\left ( x+m \right )\left ( f\left ( x \right )+\sqrt{m+1} \right )=-\left ( m+2 \right ),\forall x\in \mathbb{R},m\in \mathbb{Z^+}$

Functions $f$ satisfying $ f\circ f(x)=2f(x)-x,\forall x\in\mathbb{R}$.

Functions satisfying $\sum_{n=0}^k(-1)^n\binom{k}{k-n}f^{k-n}(x)=0$.

Math question functions help me?

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