Question

real analysis -functional equation

score 288 · Answer 1 · 2015-03-28 18:24:38

288

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real analysis -functional equation

Published on 28 Mar 2015 - 18:24

score 2.4k · Answer 2 · 2026-04-03 07:33:51

2.4k

Views

Boolean Simplification of AB + A'+B'

Published on 03 Apr 2026 - 7:33

score 121 · Answer 3 · 2015-03-29 12:38:26

121

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A function $\psi(z)$ satisfies the functional equation $\psi(z+1)=\frac{1}{z}+\psi(z)$. Prove that $\psi(\frac{1}{2})=\psi(1)-2\ln2$.

Published on 29 Mar 2015 - 12:38

score 125 · Answer 4 · 2015-04-01 08:03:03

125

Views

Solving for $f(2004)$ in a given functional equation

Published on 01 Apr 2015 - 8:03

score 113 · Answer 5 · 2015-04-01 19:00:40

113

Views

What are all pairs of functions f and g so that $f(x)f(y) = g(x+y)$?

Published on 01 Apr 2015 - 19:00

score 106 · Answer 6 · 2015-04-02 07:54:58

106

Views

hyperplane in $L^2$

Published on 02 Apr 2015 - 7:54

score 234 · Answer 7 · 2015-04-02 10:46:21

234

Views

Extension of the additive Cauchy functional equation

Published on 02 Apr 2015 - 10:46

score 109 · Answer 8 · 2015-04-05 11:13:45

109

Views

Iterative (functional) roots of integer functions (functions on $\mathbb{Z}$)

Published on 05 Apr 2015 - 11:13

score 515 · Answer 9 · 2015-04-05 13:38:21

515

Views

solving functional equation $f(x+y) +f(x)f(y)=f(x)+f(y)+f(xy)$ for all real numbers

Published on 05 Apr 2015 - 13:38

score 623 · Answer 10 · 2015-04-07 21:29:44

623

Views

Integer functional equation $f(f(f(n)))=f(n+1)+1$

Published on 07 Apr 2015 - 21:29

score 374 · Answer 11 · 2015-04-09 08:43:51

374

Views

$f \colon \mathbb{R} \rightarrow \mathbb{R}$, $f$ is continuous , and $f(x+1)+f(x)=x^2$

Published on 09 Apr 2015 - 8:43

score 203 · Answer 12 · 2015-04-10 07:14:13

203

Views

Find $f(x) $ given that: $f'(x)=\frac{f(x)-x}{f(x)+x}$

Published on 10 Apr 2015 - 7:14

score 56 · Answer 13 · 2015-04-11 21:42:46

56

Views

What are 'Regular Products'?

Published on 11 Apr 2015 - 21:42

score 127 · Answer 14 · 2026-03-28 16:44:18

127

Views

We all know about compositions of functions, but what about decomposition. Is there a way with math, not just heuristics?

Published on 28 Mar 2026 - 16:44

score 205 · Answer 15 · 2015-04-15 15:47:54

205

Views

Solve differential equation $f'(z) = e^{-2} (f(z/e))^2$

Published on 15 Apr 2015 - 15:47

List Question

real analysis -functional equation

Boolean Simplification of AB + A'+B'

A function $\psi(z)$ satisfies the functional equation $\psi(z+1)=\frac{1}{z}+\psi(z)$. Prove that $\psi(\frac{1}{2})=\psi(1)-2\ln2$.

Solving for $f(2004)$ in a given functional equation

What are all pairs of functions f and g so that $f(x)f(y) = g(x+y)$?

hyperplane in $L^2$

Extension of the additive Cauchy functional equation

Iterative (functional) roots of integer functions (functions on $\mathbb{Z}$)

solving functional equation $f(x+y) +f(x)f(y)=f(x)+f(y)+f(xy)$ for all real numbers

Integer functional equation $f(f(f(n)))=f(n+1)+1$

$f \colon \mathbb{R} \rightarrow \mathbb{R}$, $f$ is continuous , and $f(x+1)+f(x)=x^2$

Find $f(x) $ given that: $f'(x)=\frac{f(x)-x}{f(x)+x}$

What are 'Regular Products'?

We all know about compositions of functions, but what about decomposition. Is there a way with math, not just heuristics?

Solve differential equation $f'(z) = e^{-2} (f(z/e))^2$

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