List questions from functional-equations

Published on 28 Oct 2018 - 16:33

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Functional equation - Cyclic Substitutions

Published on 25 Mar 2026 - 20:07

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Help understanding an injectivity proving technique in functional equations

Published on 31 Oct 2018 - 7:41

136

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Finding all functions $ f : \mathbb N^\to\mathbb N^$ such that for every $ x , y \in \mathbb N ^ * $, $ f ( x ) + f ( y ) \mid x ^ n + y ^ n $

Published on 31 Oct 2018 - 12:01

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solving $f(x)=\frac x{1-x^2}+2(1+x)f(x^2)$ without power series expansion

Published on 31 Oct 2018 - 15:55

472

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Relation between CDF and PDF

Published on 31 Oct 2018 - 23:53

56

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Integral equation in polar coodinate system

Published on 25 Mar 2026 - 3:07

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Find all functions such that $f(x^2+y^2f(x))=xf(y)^2-f(x)^2$

Published on 01 Nov 2018 - 22:50

424

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Prove that $f$ is additive if $f(x)f(x-y)+f(y)f(x+y)= f(x)^2+f(y)^2$

Published on 02 Nov 2018 - 19:05

123

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Functional equation for the lambert w function?

Published on 24 Mar 2026 - 23:41

2k

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Determining if a differential equation has unique solution

Published on 06 Nov 2018 - 9:02

257

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Probability density function invariant under $x\mapsto 1/x$

Published on 07 Nov 2018 - 12:40

104

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Asymptotics for $ f(n) = f(n - 1) + f( n - g(n) ) $?

Published on 25 Mar 2026 - 22:30

73

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Functional Identity

Published on 25 Mar 2026 - 19:00

830

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Prove that, the function $f$ is injective: $f \big(f(x)f(y)\big) + f(x +y) = f(xy).$

Published on 12 Nov 2018 - 21:23

List Question

Determine all continuous real function which satisfies the following

Functional equation - Cyclic Substitutions

Help understanding an injectivity proving technique in functional equations

Finding all functions $ f : \mathbb N^\to\mathbb N^$ such that for every $ x , y \in \mathbb N ^ * $, $ f ( x ) + f ( y ) \mid x ^ n + y ^ n $

solving $f(x)=\frac x{1-x^2}+2(1+x)f(x^2)$ without power series expansion

Relation between CDF and PDF

Integral equation in polar coodinate system

Find all functions such that $f(x^2+y^2f(x))=xf(y)^2-f(x)^2$

Prove that $f$ is additive if $f(x)f(x-y)+f(y)f(x+y)= f(x)^2+f(y)^2$

Functional equation for the lambert w function?

Determining if a differential equation has unique solution

Probability density function invariant under $x\mapsto 1/x$

Asymptotics for $ f(n) = f(n - 1) + f( n - g(n) ) $?

Functional Identity

Prove that, the function $f$ is injective: $f \big(f(x)f(y)\big) + f(x +y) = f(xy).$

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