Question

Can a functional equation of the form: $\zeta (s)=f(s) \zeta (s+1)$ exist?

score 410 · Answer 1 · 2026-04-07 16:52:59

410

Views

Can a functional equation of the form: $\zeta (s)=f(s) \zeta (s+1)$ exist?

Published on 07 Apr 2026 - 16:52

score 128 · Answer 2 · 2017-11-06 15:35:34

128

Views

Proving that this function has the same value for all integers $\geq4$.

Published on 06 Nov 2017 - 15:35

score 34 · Answer 3 · 2017-11-06 18:52:50

34

Views

How do I calculate IRR(Internal Rate of Return) of unequal cash flows.

Published on 06 Nov 2017 - 18:52

score 108 · Answer 4 · 2017-11-08 02:45:22

Find all surjective functions $f:[0,\infty)\to[0,\infty)$ such that $f\big(xf(y)\big)f(y)=f(x+y)$, $f(2)=0$ and $f(x)\ne0$ for $0\le x<2$

score 52 · Answer 5 · 2026-04-07 20:08:44

52

Views

How to build smooth families of functions satisfying a power unity?

Published on 07 Apr 2026 - 20:08

score 104 · Answer 6 · 2017-11-10 08:55:29

104

Views

Find all functions $f: \Bbb{R} \to \Bbb{R} $ such that for every $x, y \in \mathbb R, f(x\cdot f(y)) = x\cdot y$.

Published on 10 Nov 2017 - 8:55

score 447 · Answer 7 · 2017-11-11 09:05:31

447

Views

Find the integral $\int_{0}^{1} f(x)dx$ for $f(x)+f(1-{1\over x})=\arctan x\,,\quad \forall \,x\neq 0$.

Published on 11 Nov 2017 - 9:05

score 123 · Answer 8 · 2017-11-12 15:01:53

123

Views

Find all functions : $f(x)+f(\frac{x}{2})= \frac{x}{2}$

Published on 12 Nov 2017 - 15:01

score 127 · Answer 9 · 2017-11-13 02:26:57

127

Views

simple but (seemingly?) tricky recurrence

Published on 13 Nov 2017 - 2:26

score 69 · Answer 10 · 2017-11-15 12:23:24

69

Views

Find all continuous functions $f:\mathbb{R}\longrightarrow \mathbb{R}$ so that $f(x) = f(x^2+{1\over 4})$ is valid for all $x$.

Published on 15 Nov 2017 - 12:23

score 227 · Answer 11 · 2026-03-26 06:32:56

227

Views

Sylvester's sequence, and a similar sum

Published on 26 Mar 2026 - 6:32

score 176 · Answer 12 · 2026-03-28 05:23:18

176

Views

Find all functions $f:\Bbb N\rightarrow \Bbb R $ such that: $f(m+k)=f(mk-n)$

Published on 28 Mar 2026 - 5:23

score 697 · Answer 13 · 2017-11-18 19:54:46

697

Views

If $f(x)$ satisfies $2f (x) = f(xy) + f(x/y)$, find $f(x)$

Published on 18 Nov 2017 - 19:54

score 316 · Answer 14 · 2017-11-19 08:43:58

316

Views

For function satisfying given conditions prove that $f(x). f(\frac{1}{x})=1$

Published on 19 Nov 2017 - 8:43

score 360 · Answer 15 · 2017-11-19 23:53:14

360

Views

Help with proving the surjectivity of a function satisfying $ f ( x + y ) \big( f ( x ) + f ( y ) \big) = f ( x y ) $

Published on 19 Nov 2017 - 23:53

List Question

Can a functional equation of the form: $\zeta (s)=f(s) \zeta (s+1)$ exist?

Proving that this function has the same value for all integers $\geq4$.

How do I calculate IRR(Internal Rate of Return) of unequal cash flows.

Find all surjective functions $f:[0,\infty)\to[0,\infty)$ such that $f\big(xf(y)\big)f(y)=f(x+y)$, $f(2)=0$ and $f(x)\ne0$ for $0\le x<2$

How to build smooth families of functions satisfying a power unity?

Find all functions $f: \Bbb{R} \to \Bbb{R} $ such that for every $x, y \in \mathbb R, f(x\cdot f(y)) = x\cdot y$.

Find the integral $\int_{0}^{1} f(x)dx$ for $f(x)+f(1-{1\over x})=\arctan x\,,\quad \forall \,x\neq 0$.

Find all functions : $f(x)+f(\frac{x}{2})= \frac{x}{2}$

simple but (seemingly?) tricky recurrence

Find all continuous functions $f:\mathbb{R}\longrightarrow \mathbb{R}$ so that $f(x) = f(x^2+{1\over 4})$ is valid for all $x$.

Sylvester's sequence, and a similar sum

Find all functions $f:\Bbb N\rightarrow \Bbb R $ such that: $f(m+k)=f(mk-n)$

If $f(x)$ satisfies $2f (x) = f(xy) + f(x/y)$, find $f(x)$

For function satisfying given conditions prove that $f(x). f(\frac{1}{x})=1$

Help with proving the surjectivity of a function satisfying $ f ( x + y ) \big( f ( x ) + f ( y ) \big) = f ( x y ) $

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