List questions from functional-equations

Published on 19 Nov 2023 - 17:44

95

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Can there be a finite closed form for the one dimensional heat kernel $e^{\frac{d^2}{dx^2}}$ in operator calculus?

Published on 25 Mar 2026 - 23:38

56

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Tetration and $f(x) = \exp(\int_1^x \ln(f(t)) dt)$

Published on 26 Mar 2026 - 4:53

95

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A non-local equation on Laplace transforms.

Published on 22 Nov 2023 - 14:01

257

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Thailand MO $f(x)f(y)f(x-y) = x^2f(y) - y^2f(x)$

Published on 27 Nov 2023 - 16:52

24

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Proving energy conservation from functional equations

Published on 28 Nov 2023 - 4:04

44

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Watanabe characterization of a Poisson process

Published on 28 Nov 2023 - 11:03

224

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Functional equation: $f(z) = \sum_{n=0}^{\infty} f(n)^2 z^n$?

Published on 29 Nov 2023 - 12:23

129

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$g(z) = \sum_{n=0}^{\infty} \frac{g(n)}{(n+1)!} z^n$ with $0 \leq g(n)$?

Published on 26 Mar 2026 - 22:18

137

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Is $f'(x)=f(1/x)$ solvable?

Published on 30 Nov 2023 - 15:14

184

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How solve the problem $f(x+2)=f(x)+4x+4$ for any $x$

Published on 03 Dec 2023 - 8:30

36

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Convolution power

Published on 04 Dec 2023 - 17:56

151

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Find all the polynomials $f$ that satisfy $f(x^2)+f(x)f(x+1)=0$.

Published on 05 Dec 2023 - 1:42

217

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Does there exist an $f: \mathbb{R} \to \mathbb{R}$ such that $f(f(x)) = x^3 + 1$?

Published on 05 Dec 2023 - 9:58

100

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How can you get the result of $f(2015) + g(2015)$?

Published on 05 Dec 2023 - 17:12

List Question

Functional equation f(x+1)=f(x)+2x+1

Can there be a finite closed form for the one dimensional heat kernel $e^{\frac{d^2}{dx^2}}$ in operator calculus?

Tetration and $f(x) = \exp(\int_1^x \ln(f(t)) dt)$

A non-local equation on Laplace transforms.

Thailand MO $f(x)f(y)f(x-y) = x^2f(y) - y^2f(x)$

Proving energy conservation from functional equations

Watanabe characterization of a Poisson process

Functional equation: $f(z) = \sum_{n=0}^{\infty} f(n)^2 z^n$?

$g(z) = \sum_{n=0}^{\infty} \frac{g(n)}{(n+1)!} z^n$ with $0 \leq g(n)$?

Is $f'(x)=f(1/x)$ solvable?

How solve the problem $f(x+2)=f(x)+4x+4$ for any $x$

Convolution power

Find all the polynomials $f$ that satisfy $f(x^2)+f(x)f(x+1)=0$.

Does there exist an $f: \mathbb{R} \to \mathbb{R}$ such that $f(f(x)) = x^3 + 1$?

How can you get the result of $f(2015) + g(2015)$?

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