Question

Factorial-like interpolation problem: looking for a function that satisfies $f(x) - f(x - 1) = \frac{\sin (πx)}{πx}$

score 177 · Answer 1 · 2026-04-16 08:23:45

177

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Factorial-like interpolation problem: looking for a function that satisfies $f(x) - f(x - 1) = \frac{\sin (πx)}{πx}$

Published on 16 Apr 2026 - 8:23

score 82 · Answer 2 · 2026-04-11 00:45:14

82

Views

Minimizing a functional with inequality constraints

Published on 11 Apr 2026 - 0:45

score 205 · Answer 3 · 2026-04-11 21:27:24

205

Views

What does the functional equation of the $\zeta$ function states?

Published on 11 Apr 2026 - 21:27

score 78 · Answer 4 · 2026-04-17 11:12:22

Functional equation: $f:\mathbb R\to\mathbb R$ and $g:]0,\infty[\to\mathbb R$ such that $f(\ln x+\alpha\ln y)=g(\sqrt x)+g(\sqrt y)\quad\forall x,y>0$

score 74 · Answer 5 · 2026-04-11 20:02:33

74

Views

Usage of induction to evaluate a function

Published on 11 Apr 2026 - 20:02

score 388 · Answer 6 · 2026-04-15 13:35:08

388

Views

Solving $f(x+f(y)) = f(x) + y$

Published on 15 Apr 2026 - 13:35

score 107 · Answer 7 · 2026-04-17 06:29:13

107

Views

Showing $\frac{\sinh t}{\sinh T}$ extremises the functional $S[x]=\int_0^T\big(\dot x(t)^2+x(t)^2\big)\ \mathrm dt$ with given boundary conditions

Published on 17 Apr 2026 - 6:29

score 124 · Answer 8 · 2026-04-17 04:45:34

finding all the functions $ f : \mathbb N \to \mathbb N $ that satisfy $ f ( n ) + f ( m ) \mathrel {\big|} n ^ 2 + k f ( n ) m + f ( m ) ^ 2 $

score 65 · Answer 9 · 2026-04-16 04:33:45

65

Views

Prove for $f: \mathbb Q \to \mathbb R$ $f(x+f(y)) = f(x) + y$ that $f$ is injective

Published on 16 Apr 2026 - 4:33

score 163 · Answer 10 · 2026-04-16 04:28:18

163

Views

Find all positive differentiable functions $f$ that satisfy $\int_0^x \sin(t) f(t) dt = [f(x)]^2-1$for all real numbers $x$.

Published on 16 Apr 2026 - 4:28

score 58 · Answer 11 · 2026-04-15 08:31:07

58

Views

Finding all solutions to the functional equation $-\frac{1}{2}f(t,x) = f(2t, -x)$

Published on 15 Apr 2026 - 8:31

score 2.6k · Answer 12 · 2026-04-13 22:23:32

2.6k

Views

Is a function that preserves the cross product necessarily linear in $\mathbb R^3$? $f(a) \times f(b) = a \times b$

Published on 13 Apr 2026 - 22:23

score 481 · Answer 13 · 2026-04-13 19:54:15

481

Views

Parallelogram law functional equation: $ f ( x + y ) + f ( x - y ) = 2 \big( f ( x ) + f ( y ) \big) $

Published on 13 Apr 2026 - 19:54

score 45 · Answer 14 · 2026-04-13 02:27:47

45

Views

Weak convergene in Hilbert space

Published on 13 Apr 2026 - 2:27

score 128 · Answer 15 · 2026-04-15 13:26:38

128

Views

Find all functions $ \mathbb{Z} \mapsto \mathbb{Z} $ such that $f(a-b+f(b))=f(a)+f(b)$

Published on 15 Apr 2026 - 13:26

List Question

Factorial-like interpolation problem: looking for a function that satisfies $f(x) - f(x - 1) = \frac{\sin (πx)}{πx}$

Minimizing a functional with inequality constraints

What does the functional equation of the $\zeta$ function states?

Functional equation: $f:\mathbb R\to\mathbb R$ and $g:]0,\infty[\to\mathbb R$ such that $f(\ln x+\alpha\ln y)=g(\sqrt x)+g(\sqrt y)\quad\forall x,y>0$

Usage of induction to evaluate a function

Solving $f(x+f(y)) = f(x) + y$

Showing $\frac{\sinh t}{\sinh T}$ extremises the functional $S[x]=\int_0^T\big(\dot x(t)^2+x(t)^2\big)\ \mathrm dt$ with given boundary conditions

finding all the functions $ f : \mathbb N \to \mathbb N $ that satisfy $ f ( n ) + f ( m ) \mathrel {\big|} n ^ 2 + k f ( n ) m + f ( m ) ^ 2 $

Prove for $f: \mathbb Q \to \mathbb R$ $f(x+f(y)) = f(x) + y$ that $f$ is injective

Find all positive differentiable functions $f$ that satisfy $\int_0^x \sin(t) f(t) dt = [f(x)]^2-1$for all real numbers $x$.

Finding all solutions to the functional equation $-\frac{1}{2}f(t,x) = f(2t, -x)$

Is a function that preserves the cross product necessarily linear in $\mathbb R^3$? $f(a) \times f(b) = a \times b$

Parallelogram law functional equation: $ f ( x + y ) + f ( x - y ) = 2 \big( f ( x ) + f ( y ) \big) $

Weak convergene in Hilbert space

Find all functions $ \mathbb{Z} \mapsto \mathbb{Z} $ such that $f(a-b+f(b))=f(a)+f(b)$

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