Question

Which functions $f$ satisfy $f(x-a-c)f(x-b)=\alpha f(x-c-\tfrac{a+b}{2})f(x-\tfrac{a+b}{2})$ for every $x$ where $a,b,c,\alpha$ are constants?

score 86 · Answer 1 · 2021-04-18 12:46:10

86

Views

Which functions $f$ satisfy $f(x-a-c)f(x-b)=\alpha f(x-c-\tfrac{a+b}{2})f(x-\tfrac{a+b}{2})$ for every $x$ where $a,b,c,\alpha$ are constants?

Published on 18 Apr 2021 - 12:46

score 110 · Answer 2 · 2021-04-23 13:45:20

110

Views

Given that ◦ is a bijection, prove that itself must be a bijection

Published on 23 Apr 2021 - 13:45

score 371 · Answer 3 · 2021-04-26 19:05:16

371

Views

An elementary function with asymptotic $f'(x)\sim2f(2x)$ for $x\to0^+$

Published on 26 Apr 2021 - 19:05

score 47 · Answer 4 · 2021-05-06 11:11:49

47

Views

Surjective Functions. Beginner in discrete Mathematics

Published on 06 May 2021 - 11:11

score 47 · Answer 5 · 2021-05-17 17:58:28

47

Views

Which ODEs have solutions in terms of elementary functions?

Published on 17 May 2021 - 17:58

score 80 · Answer 6 · 2021-05-30 19:24:53

Basic: $x^2 - 1$ and $-x^2 + 1$ have the same roots and therefore both could be written as $(x+1)(x-1).$ I guess that’s not right...

score 116 · Answer 7 · 2021-05-31 12:36:50

116

Views

Solve equation $a\exp({k_{1}x}) - b\exp({k_{2}x}) + c = 0$

Published on 31 May 2021 - 12:36

score 218 · Answer 8 · 2026-02-23 19:19:46

218

Views

Derive Euler's formula $e^{ix}=\cos{x}+i\sin{x}$ and estimate $e$ in an elementary way

Published on 23 Feb 2026 - 19:19

score 685 · Answer 9 · 2026-02-24 00:42:33

685

Views

Is it decidable whether the value of a given definite integral has a closed-form expression?

Published on 24 Feb 2026 - 0:42

score 49 · Answer 10 · 2021-06-25 09:33:40

49

Views

Besides circles, are there other curves for which $\vec{r}'(t)$ and $\vec{r}''(t)$ are always perpendicular, described by only elementary functions?

Published on 25 Jun 2021 - 9:33

score 73 · Answer 11 · 2021-06-25 11:47:13

73

Views

Solutions of $ 5^x+5^{x^2}=4^x+6^{x^2} \quad \left(x\in \mathbb{R}\right)$

Published on 25 Jun 2021 - 11:47

score 238 · Answer 12 · 2026-03-26 22:52:35

238

Views

Is there a method for solving equations like $\sin x=x\cos(x)$ in closed form?

Published on 26 Mar 2026 - 22:52

score 148 · Answer 13 · 2026-02-23 07:48:07

148

Views

Why can't $a=\theta-\sin(\theta)$ be solved for $\theta$ in terms of $a$ in closed form?

Published on 23 Feb 2026 - 7:48

score 83 · Answer 14 · 2021-07-25 02:47:08

83

Views

Proving this polynomial is irreducible

Published on 25 Jul 2021 - 2:47

score 65 · Answer 15 · 2021-07-27 03:28:34

65

Views

Inequality for convex function / Jensen's inequality

Published on 27 Jul 2021 - 3:28

List Question

Which functions $f$ satisfy $f(x-a-c)f(x-b)=\alpha f(x-c-\tfrac{a+b}{2})f(x-\tfrac{a+b}{2})$ for every $x$ where $a,b,c,\alpha$ are constants?

Given that ◦ is a bijection, prove that itself must be a bijection

An elementary function with asymptotic $f'(x)\sim2f(2x)$ for $x\to0^+$

Surjective Functions. Beginner in discrete Mathematics

Which ODEs have solutions in terms of elementary functions?

Basic: $x^2 - 1$ and $-x^2 + 1$ have the same roots and therefore both could be written as $(x+1)(x-1).$ I guess that’s not right...

Solve equation $a\exp({k_{1}x}) - b\exp({k_{2}x}) + c = 0$

Derive Euler's formula $e^{ix}=\cos{x}+i\sin{x}$ and estimate $e$ in an elementary way

Is it decidable whether the value of a given definite integral has a closed-form expression?

Besides circles, are there other curves for which $\vec{r}'(t)$ and $\vec{r}''(t)$ are always perpendicular, described by only elementary functions?

Solutions of $ 5^x+5^{x^2}=4^x+6^{x^2} \quad \left(x\in \mathbb{R}\right)$

Is there a method for solving equations like $\sin x=x\cos(x)$ in closed form?

Why can't $a=\theta-\sin(\theta)$ be solved for $\theta$ in terms of $a$ in closed form?

Proving this polynomial is irreducible

Inequality for convex function / Jensen's inequality

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