Question

Solve for $z$, $ z = \int\frac{p(x)}{x-z^*}\mathrm{d}x $

score 61 · Answer 1 · 2026-03-26 16:05:56

61

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Solve for $z$, $ z = \int\frac{p(x)}{x-z^*}\mathrm{d}x $

Published on 26 Mar 2026 - 16:05

score 1.5k · Answer 2 · 2020-06-13 21:14:16

1.5k

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Functions $f: \mathbb{Z}^{+}\to \mathbb{R}$ satisfying $x f(y) + y f(x) = (x+y) f(x^2+y^2)$

Published on 13 Jun 2020 - 21:14

score 72 · Answer 3 · 2026-03-30 05:31:34

72

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Functional Equation and Calculus

Published on 30 Mar 2026 - 5:31

score 76 · Answer 4 · 2020-06-16 04:13:31

76

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General solutions for a functional equation

Published on 16 Jun 2020 - 4:13

score 40 · Answer 5 · 2020-06-16 07:39:09

40

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Show that for every positive integer $n$ $ \phi^{n}(x)=\left(c+f(c)+f^{2}(c)+\ldots . .+f^{n-1}(c)\right)+f^{n}(x) $

Published on 16 Jun 2020 - 7:39

score 65 · Answer 6 · 2020-06-16 16:06:43

65

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Finding $|f(4)|$ given that $f$ is a continuous function satisfying $f(x)+f(2x+y)+5xy=f(3x-y)+2x^2+1\forall x,y\in\mathbb{R}$

Published on 16 Jun 2020 - 16:06

score 110 · Answer 7 · 2020-06-16 18:24:59

110

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Analytic solutions to $f(5 x + x^3) = f(5 x) + f(3 x)$?

Published on 16 Jun 2020 - 18:24

score 150 · Answer 8 · 2026-03-26 22:51:44

150

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Using Euler-Lagrange equations to prove Cauchy's Theorem

Published on 26 Mar 2026 - 22:51

score 168 · Answer 9 · 2020-06-18 13:42:32

168

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How to solve this Functional Equation: $f(x+1) - f(x) = e^{ax}$?

Published on 18 Jun 2020 - 13:42

score 48 · Answer 10 · 2026-03-27 04:16:35

48

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How to prove that this function over nonnegative integers is monotonic?

Published on 27 Mar 2026 - 4:16

score 69 · Answer 11 · 2020-06-22 07:15:20

69

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About the polynomials satisfying $P\left((x-y)^2\right)+P\left((y-z)^2\right)+P\left((z-x)^2\right)=18P\left(\left(\frac{(x+y+z)^2}3\right)^2\right)$

Published on 22 Jun 2020 - 7:15

score 75 · Answer 12 · 2026-03-26 17:29:27

75

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General strategies for solving functional equations.

Published on 26 Mar 2026 - 17:29

score 88 · Answer 13 · 2026-03-25 11:32:30

88

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How can I prove this functional equation?

Published on 25 Mar 2026 - 11:32

score 202 · Answer 14 · 2026-03-25 18:50:37

202

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$f(xy + x +y) = f(xy) + f(x) + f(y)$ and $f(x)(y - x) + f(y)(x - y) \geq 0$.

Published on 25 Mar 2026 - 18:50

score 108 · Answer 15 · 2026-03-30 17:08:13

108

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Residues of the (modern) Approximate Functional Equation

Published on 30 Mar 2026 - 17:08

List Question

Solve for $z$, $ z = \int\frac{p(x)}{x-z^*}\mathrm{d}x $

Functions $f: \mathbb{Z}^{+}\to \mathbb{R}$ satisfying $x f(y) + y f(x) = (x+y) f(x^2+y^2)$

Functional Equation and Calculus

General solutions for a functional equation

Show that for every positive integer $n$ $ \phi^{n}(x)=\left(c+f(c)+f^{2}(c)+\ldots . .+f^{n-1}(c)\right)+f^{n}(x) $

Finding $|f(4)|$ given that $f$ is a continuous function satisfying $f(x)+f(2x+y)+5xy=f(3x-y)+2x^2+1\forall x,y\in\mathbb{R}$

Analytic solutions to $f(5 x + x^3) = f(5 x) + f(3 x)$?

Using Euler-Lagrange equations to prove Cauchy's Theorem

How to solve this Functional Equation: $f(x+1) - f(x) = e^{ax}$?

How to prove that this function over nonnegative integers is monotonic?

About the polynomials satisfying $P\left((x-y)^2\right)+P\left((y-z)^2\right)+P\left((z-x)^2\right)=18P\left(\left(\frac{(x+y+z)^2}3\right)^2\right)$

General strategies for solving functional equations.

How can I prove this functional equation?

$f(xy + x +y) = f(xy) + f(x) + f(y)$ and $f(x)(y - x) + f(y)(x - y) \geq 0$.

Residues of the (modern) Approximate Functional Equation

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