Question

Prove $f(x)\cdot f\left( \frac{1}{x}\right)=1$

score 149 · Answer 1 · 2023-06-03 15:19:23

149

Views

Prove $f(x)\cdot f\left( \frac{1}{x}\right)=1$

Published on 03 Jun 2023 - 15:19

score 86 · Answer 2 · 2023-06-10 13:38:47

86

Views

Solution(s?) of the functional equation $f(2f(x)) = 2x$

Published on 10 Jun 2023 - 13:38

score 75 · Answer 3 · 2023-06-10 22:19:09

75

Views

The functional differential equation : $f '(x) = a f(x/3)^2 + h f(x/4) + b$

Published on 10 Jun 2023 - 22:19

score 16 · Answer 4 · 2026-03-26 12:37:18

16

Views

Solutions for $Re(z) > 2$ ,$f(z) = \sum_{1<i}^{\infty} f(i)^{\dfrac{z-i+1}{i}}$?

Published on 26 Mar 2026 - 12:37

score 69 · Answer 5 · 2023-06-11 23:20:21

69

Views

Solutions to $f(x+1) = 1 + f(x) + f(x/2)^2 + f(x/3)^3 + f(x/4)^4+...$ ? $f(x) = O(\frac{\exp(x)}{x+1})$?

Published on 11 Jun 2023 - 23:20

score 96 · Answer 6 · 2026-03-25 20:11:00

96

Views

On the solution to $u'(x)=2u(2x+1)-2u(2x-1)$ and the Fabius function

Published on 25 Mar 2026 - 20:11

score 67 · Answer 7 · 2026-03-26 01:28:26

67

Views

$L^1\big((1+x)\mathrm dx\big)$ form

Published on 26 Mar 2026 - 1:28

score 83 · Answer 8 · 2023-06-13 08:47:12

83

Views

What is the closed form of the infinite series $g(x) = \sum_{r=1}^{\infty} x^{3^{r}}$ for $|x|<1$?

Published on 13 Jun 2023 - 8:47

score 19 · Answer 9 · 2026-03-28 21:44:22

19

Views

Existence of Coupled Functions Defined via Probability Distributions and Their Derivatives

Published on 28 Mar 2026 - 21:44

score 87 · Answer 10 · 2023-06-13 15:28:19

87

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Find all functions $f: \mathbb{N} \rightarrow \mathbb{N}$ such that $f(n)+2f(f(n))=3n+5$

Published on 13 Jun 2023 - 15:28

score 121 · Answer 11 · 2026-03-31 22:46:05

121

Views

What functions satisfy $f(x+1)+f(x-1)=x$?

Published on 31 Mar 2026 - 22:46

score 131 · Answer 12 · 2023-06-19 19:33:36

131

Views

Find all continuous functions from $\mathbb{R}$ to $\mathbb{R}$ such that $(f(x+y))^2-(f(x-y))^2=4f(x)f(y)$

Published on 19 Jun 2023 - 19:33

score 150 · Answer 13 · 2023-06-20 02:17:06

150

Views

Understanding Hershel-Maxwell derivation of the normal distribution

Published on 20 Jun 2023 - 2:17

score 143 · Answer 14 · 2023-06-21 21:16:00

143

Views

A function in $L^1(\mathbb{R}^d)$ satisfying $f(x)+f\ast g(x)=e^{-|x|^2}.$

Published on 21 Jun 2023 - 21:16

score 440 · Answer 15 · 2023-06-24 23:39:06

440

Views

$f(x) + f(x/2) + f(x/3) + f(x/4) + ... = x$ and $\lim_{n \to \infty} \frac{f(n)}{\pi(n)} = 1$?

Published on 24 Jun 2023 - 23:39

List Question

Prove $f(x)\cdot f\left( \frac{1}{x}\right)=1$

Solution(s?) of the functional equation $f(2f(x)) = 2x$

The functional differential equation : $f '(x) = a f(x/3)^2 + h f(x/4) + b$

Solutions for $Re(z) > 2$ ,$f(z) = \sum_{1<i}^{\infty} f(i)^{\dfrac{z-i+1}{i}}$?

Solutions to $f(x+1) = 1 + f(x) + f(x/2)^2 + f(x/3)^3 + f(x/4)^4+...$ ? $f(x) = O(\frac{\exp(x)}{x+1})$?

On the solution to $u'(x)=2u(2x+1)-2u(2x-1)$ and the Fabius function

$L^1\big((1+x)\mathrm dx\big)$ form

What is the closed form of the infinite series $g(x) = \sum_{r=1}^{\infty} x^{3^{r}}$ for $|x|<1$?

Existence of Coupled Functions Defined via Probability Distributions and Their Derivatives

Find all functions $f: \mathbb{N} \rightarrow \mathbb{N}$ such that $f(n)+2f(f(n))=3n+5$

What functions satisfy $f(x+1)+f(x-1)=x$?

Find all continuous functions from $\mathbb{R}$ to $\mathbb{R}$ such that $(f(x+y))^2-(f(x-y))^2=4f(x)f(y)$

Understanding Hershel-Maxwell derivation of the normal distribution

A function in $L^1(\mathbb{R}^d)$ satisfying $f(x)+f\ast g(x)=e^{-|x|^2}.$

$f(x) + f(x/2) + f(x/3) + f(x/4) + ... = x$ and $\lim_{n \to \infty} \frac{f(n)}{\pi(n)} = 1$?

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