List questions from functional-equations

Published on 12 Nov 2010 - 20:16

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Find a function such that $f(\log(x)) = x \cdot f(x) $

Published on 19 Nov 2010 - 15:29

206

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conversion of a powerseries $-3x+4x^2-5x^3+\ldots $ into $ -2+\frac 1 x - 0 - \frac 1 {x^3} + \ldots $

Published on 23 Nov 2010 - 19:58

154

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How to solve the following system?

Published on 09 Dec 2010 - 21:33

4.6k

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On sort-of-linear functions: does $f(x+y) = f(x) + f(y)$ imply $f(\alpha x) = \alpha f(x)$?

Published on 02 Jan 2011 - 23:15

5.6k

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$f(x) + f(1-x) = f(1)$

Published on 08 Jan 2011 - 22:49

610

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Evaluating $f(x) f(x/2) f(x/4) f(x/8) \cdots$

Published on 02 Apr 2026 - 3:50

98

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Function Shape Reference

Published on 12 Jan 2011 - 13:01

784

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Solving the functional equation $f(x+1) - f(x-1) = g(x)$

Published on 13 Jan 2011 - 1:45

270

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Solving the functional equation $x[f(x+1)-f(x-1)]=1$

Published on 19 Jan 2011 - 16:53

186

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$x^3[f(x+1)-f(x-1)]=1$

Published on 19 Jan 2011 - 17:24

146

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$x^3[f(x+1)-f(x)]=1$

Published on 19 Jan 2011 - 18:03

972

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The Notorious Triangle Problem

Published on 23 Jan 2011 - 18:18

583

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$f(x+f(y))=f(x-f(y))+4xf(y)$

Published on 26 Jan 2011 - 23:08

263

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$f(1-f(x))=f(x)$

Published on 27 Jan 2011 - 23:09

List Question

Solve the functional equation $f (x+y)=f (x)+f (y)+xy (x+y)$, $f$ continuous at $0$

Find a function such that $f(\log(x)) = x \cdot f(x) $

conversion of a powerseries $-3x+4x^2-5x^3+\ldots $ into $ -2+\frac 1 x - 0 - \frac 1 {x^3} + \ldots $

How to solve the following system?

On sort-of-linear functions: does $f(x+y) = f(x) + f(y)$ imply $f(\alpha x) = \alpha f(x)$?

$f(x) + f(1-x) = f(1)$

Evaluating $f(x) f(x/2) f(x/4) f(x/8) \cdots$

Function Shape Reference

Solving the functional equation $f(x+1) - f(x-1) = g(x)$

Solving the functional equation $x[f(x+1)-f(x-1)]=1$

$x^3[f(x+1)-f(x-1)]=1$

$x^3[f(x+1)-f(x)]=1$

The Notorious Triangle Problem

$f(x+f(y))=f(x-f(y))+4xf(y)$

$f(1-f(x))=f(x)$

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