Question

Solving recurrence relation with generating functions

score 125 · Answer 1 · 2023-10-04 18:46:26

125

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Solving recurrence relation with generating functions

Published on 04 Oct 2023 - 18:46

score 48 · Answer 2 · 2026-03-30 03:34:24

48

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Functional Equation Solution?

Published on 30 Mar 2026 - 3:34

score 91 · Answer 3 · 2023-10-05 16:42:39

91

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functional equation $f∘f(x)=x^{\ln^3x}$

Published on 05 Oct 2023 - 16:42

score 44 · Answer 4 · 2023-10-06 14:17:40

44

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Trying to generalize the solving of a functional equation

Published on 06 Oct 2023 - 14:17

score 127 · Answer 5 · 2023-10-07 17:20:10

127

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Find all functions $f:R_{+}\rightarrow R_{+}$ such that for all $x,y\in R_{+}, f(x)=f(f(f(x))+y)+f(xf(y))f(x+y).$

Published on 07 Oct 2023 - 17:20

score 127 · Answer 6 · 2026-04-01 21:32:40

127

Views

Is there a function which graphs the exact same curve in both polar and Cartesian coordinate systems?

Published on 01 Apr 2026 - 21:32

score 100 · Answer 7 · 2026-03-25 21:49:29

100

Views

References for equations like $f(n) = f^{(n)}(0) $?

Published on 25 Mar 2026 - 21:49

score 21 · Answer 8 · 2023-10-16 05:17:51

21

Views

Find all integer-valued functions f(n) taking values in the integers satisfying the equation f[f(n)]=n+1

Published on 16 Oct 2023 - 5:17

score 187 · Answer 9 · 2023-10-16 13:46:56

187

Views

Find all functions $f\colon \mathbb{R} \to \mathbb{R}$ such that $f(af(b) − b^2) = (b + 1)f(a − b)$ for all reals $a$ and $b$

Published on 16 Oct 2023 - 13:46

score 48 · Answer 10 · 2026-03-30 11:41:19

48

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prove there doesn't exist a nonconstant rational function f with real coefficients so that $f(x^2/(x+1))$ is a real polynomial

Published on 30 Mar 2026 - 11:41

score 111 · Answer 11 · 2023-10-20 20:48:33

111

Views

How to solve $f(x) = x^3 - f(2x)$

Published on 20 Oct 2023 - 20:48

score 102 · Answer 12 · 2023-10-21 18:33:40

102

Views

How to solve $(x-2)f(y)+f(y+2f(x)) = f(x + yf(x))$?

Published on 21 Oct 2023 - 18:33

score 109 · Answer 13 · 2023-10-22 15:20:15

109

Views

Are there any real analytic functions such that $\sum_{n=1}^{\infty} \frac{1}{f(n)} = \sum_{k=2}^{\infty} f(k) \left( \zeta(k) - 1 \right) $?

Published on 22 Oct 2023 - 15:20

score 129 · Answer 14 · 2023-10-22 15:27:31

129

Views

The functional differential equation $f'(x) = f(f(x))$

Published on 22 Oct 2023 - 15:27

score 830 · Answer 15 · 2026-03-26 21:54:00

830

Views

Find all entire functions that satisfy the following equality

Published on 26 Mar 2026 - 21:54

List Question

Solving recurrence relation with generating functions

Functional Equation Solution?

functional equation $f∘f(x)=x^{\ln^3x}$

Trying to generalize the solving of a functional equation

Find all functions $f:R_{+}\rightarrow R_{+}$ such that for all $x,y\in R_{+}, f(x)=f(f(f(x))+y)+f(xf(y))f(x+y).$

Is there a function which graphs the exact same curve in both polar and Cartesian coordinate systems?

References for equations like $f(n) = f^{(n)}(0) $?

Find all integer-valued functions f(n) taking values in the integers satisfying the equation f[f(n)]=n+1

Find all functions $f\colon \mathbb{R} \to \mathbb{R}$ such that $f(af(b) − b^2) = (b + 1)f(a − b)$ for all reals $a$ and $b$

prove there doesn't exist a nonconstant rational function f with real coefficients so that $f(x^2/(x+1))$ is a real polynomial

How to solve $f(x) = x^3 - f(2x)$

How to solve $(x-2)f(y)+f(y+2f(x)) = f(x + yf(x))$?

Are there any real analytic functions such that $\sum_{n=1}^{\infty} \frac{1}{f(n)} = \sum_{k=2}^{\infty} f(k) \left( \zeta(k) - 1 \right) $?

The functional differential equation $f'(x) = f(f(x))$

Find all entire functions that satisfy the following equality

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