Question

How can I solve $\sum_{b=0}^{\frac{k}{\sqrt{x}}}\sum_{a=1}^{x} \frac{aF(r\sqrt{a^2+b^2})}{\sqrt{a^2+b^2}}=cF(\delta(x+l))$ for the function $F(x)$?

score 50 · Answer 1 · 2026-04-13 16:23:09

50

Views

How can I solve $\sum_{b=0}^{\frac{k}{\sqrt{x}}}\sum_{a=1}^{x} \frac{aF(r\sqrt{a^2+b^2})}{\sqrt{a^2+b^2}}=cF(\delta(x+l))$ for the function $F(x)$?

Published on 13 Apr 2026 - 16:23

score 140 · Answer 2 · 2026-04-17 07:52:19

140

Views

Find all $f(x)$ such that $x(f(x+1)-f(x))=f(x)$

Published on 17 Apr 2026 - 7:52

score 146 · Answer 3 · 2026-04-15 16:42:11

146

Views

What is the derivative of $f(x)$ if $f(x)+f(y)=f\left(\frac{x+y}{1-xy}\right)$?

Published on 15 Apr 2026 - 16:42

score 169 · Answer 4 · 2026-04-15 16:22:39

169

Views

Find $f: \mathbb{R} \to \mathbb{R}$ which satisfies $f(2x^2+2yf(z))=2xf(x)+2zf(y).$

Published on 15 Apr 2026 - 16:22

score 203 · Answer 5 · 2026-04-17 10:53:38

203

Views

If $\frac{f(x^2)}{f(x)}=1+x+x^2+\ldots+x^7$ then what is $f(x)$?

Published on 17 Apr 2026 - 10:53

score 347 · Answer 6 · 2026-04-15 02:26:42

347

Views

Solution to the functional equation $f(2x) = f(x)\cdot\sin(x)$?

Published on 15 Apr 2026 - 2:26

score 153 · Answer 7 · 2026-04-16 16:28:04

153

Views

Finding all polynomials $P(x) \in \mathbb R[x]$ such that $P(x)^2=4P\left(x^2-5x+1\right)+2$

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score 216 · Answer 8 · 2026-04-16 13:49:18

216

Views

Nowhere continuous functions $f: \mathbb{R} \to \mathbb{R}$ such that $f\bigl(f(x)\bigr) = \frac{f(2x)}{2}$

Published on 16 Apr 2026 - 13:49

score 342 · Answer 9 · 2026-04-15 03:07:04

342

Views

Can every functional equation be solved or proved unsolvable?

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score 265 · Answer 10 · 2026-04-11 11:19:42

265

Views

The existence of bounded linear functional on a complex Hilbert space

Published on 11 Apr 2026 - 11:19

score 170 · Answer 11 · 2026-04-14 05:02:56

170

Views

Which functions share a certain property of sinusoids?

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score 131 · Answer 12 · 2026-04-17 01:18:22

Determining all the functions $f:\mathbb{R}\to\mathbb{R}$ with the property $f\bigl(x-f(y)\bigr) f\bigl(f(x)+y\bigr)=x f(x) - y f(y)$

score 114 · Answer 13 · 2026-04-17 05:33:04

114

Views

Find all functions such that $f\left(x^2+y\right)=f(x)^2+\frac{f(xy)}{f(x)}$ in $\mathbb R^*$

Published on 17 Apr 2026 - 5:33

score 110 · Answer 14 · 2026-04-14 03:21:10

110

Views

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Published on 14 Apr 2026 - 3:21

score 50 · Answer 15 · 2026-04-13 18:47:37

50

Views

Showing these are the only functions in "Find All"

Published on 13 Apr 2026 - 18:47

List Question

How can I solve $\sum_{b=0}^{\frac{k}{\sqrt{x}}}\sum_{a=1}^{x} \frac{aF(r\sqrt{a^2+b^2})}{\sqrt{a^2+b^2}}=cF(\delta(x+l))$ for the function $F(x)$?

Find all $f(x)$ such that $x(f(x+1)-f(x))=f(x)$

What is the derivative of $f(x)$ if $f(x)+f(y)=f\left(\frac{x+y}{1-xy}\right)$?

Find $f: \mathbb{R} \to \mathbb{R}$ which satisfies $f(2x^2+2yf(z))=2xf(x)+2zf(y).$

If $\frac{f(x^2)}{f(x)}=1+x+x^2+\ldots+x^7$ then what is $f(x)$?

Solution to the functional equation $f(2x) = f(x)\cdot\sin(x)$?

Finding all polynomials $P(x) \in \mathbb R[x]$ such that $P(x)^2=4P\left(x^2-5x+1\right)+2$

Nowhere continuous functions $f: \mathbb{R} \to \mathbb{R}$ such that $f\bigl(f(x)\bigr) = \frac{f(2x)}{2}$

Can every functional equation be solved or proved unsolvable?

The existence of bounded linear functional on a complex Hilbert space

Which functions share a certain property of sinusoids?

Determining all the functions $f:\mathbb{R}\to\mathbb{R}$ with the property $f\bigl(x-f(y)\bigr) f\bigl(f(x)+y\bigr)=x f(x) - y f(y)$

Find all functions such that $f\left(x^2+y\right)=f(x)^2+\frac{f(xy)}{f(x)}$ in $\mathbb R^*$

Decomposing an intensity spectrum as a superposition of blackbody spectra

Showing these are the only functions in "Find All"

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