Question

Prove with $L(x) = \int_1^x\frac{1}{t}dt$ for $x>0$ that $L(xy) = L(x)+L(y)$

score 291 · Answer 1 · 2017-06-21 13:51:15

291

Views

Prove with $L(x) = \int_1^x\frac{1}{t}dt$ for $x>0$ that $L(xy) = L(x)+L(y)$

Published on 21 Jun 2017 - 13:51

score 210 · Answer 2 · 2017-06-22 11:33:41

210

Views

Functional Equation Problem: Strictly Increasing $ f $ satisfying $ f \big( f ( n ) \big) = n + 2 $

Published on 22 Jun 2017 - 11:33

score 25 · Answer 3 · 2017-06-23 09:52:48

25

Views

A functional equation, and what to do when branches appear.

Published on 23 Jun 2017 - 9:52

score 79 · Answer 4 · 2017-06-28 13:58:44

79

Views

Functional equation $f\left(\frac{x+3f(x)}{4}\right)=x$

Published on 28 Jun 2017 - 13:58

score 495 · Answer 5 · 2017-06-30 16:13:29

495

Views

Functional Equations with Taylor Series

Published on 30 Jun 2017 - 16:13

score 164 · Answer 6 · 2017-07-01 06:04:54

164

Views

Proof verification: system of functional equations: $f(0)=1$, $f\bigl(f(n)\bigr)=n$ and $f\bigl(f(n+2)+2\bigr)=n$

Published on 01 Jul 2017 - 6:04

score 76 · Answer 7 · 2017-07-01 15:10:42

76

Views

How to find the derivative of function using given functional equation?

Published on 01 Jul 2017 - 15:10

score 178 · Answer 8 · 2017-07-01 17:43:20

178

Views

Find a function which satisfies the relation $f(x+1)=(f(x)+1)^{1/2}$

Published on 01 Jul 2017 - 17:43

score 60 · Answer 9 · 2017-07-02 13:47:28

60

Views

Functional equation hint. How to start?

Published on 02 Jul 2017 - 13:47

score 109 · Answer 10 · 2017-07-02 14:44:13

109

Views

How to solve these functional equations $f(x) = 1 + f(x) + f(x^2) + \ldots $ and $f(x) = 1 + f(x) + \big(f(x^2)\big)^2 + \ldots $?

Published on 02 Jul 2017 - 14:44

score 86 · Answer 11 · 2017-07-02 20:00:16

86

Views

$g(g(n)) = d(n)$ for all $n \in \mathbb{N}^*$

Published on 02 Jul 2017 - 20:00

score 168 · Answer 12 · 2017-07-02 22:45:22

168

Views

All functions that satisfy $f(x)^n = f(x^n)$

Published on 02 Jul 2017 - 22:45

score 107 · Answer 13 · 2017-07-04 02:08:21

107

Views

second derivative of a function equals a power of said function

Published on 04 Jul 2017 - 2:08

score 90 · Answer 14 · 2017-07-04 08:33:21

90

Views

How to solve $F(z,q) = q + z F(z,q) + z^2 \big( F(z,q^2) \big)^2$?

Published on 04 Jul 2017 - 8:33

score 95 · Answer 15 · 2017-07-05 15:15:08

95

Views

Functional Square Root Grapher

Published on 05 Jul 2017 - 15:15

List Question

Prove with $L(x) = \int_1^x\frac{1}{t}dt$ for $x>0$ that $L(xy) = L(x)+L(y)$

Functional Equation Problem: Strictly Increasing $ f $ satisfying $ f \big( f ( n ) \big) = n + 2 $

A functional equation, and what to do when branches appear.

Functional equation $f\left(\frac{x+3f(x)}{4}\right)=x$

Functional Equations with Taylor Series

Proof verification: system of functional equations: $f(0)=1$, $f\bigl(f(n)\bigr)=n$ and $f\bigl(f(n+2)+2\bigr)=n$

How to find the derivative of function using given functional equation?

Find a function which satisfies the relation $f(x+1)=(f(x)+1)^{1/2}$

Functional equation hint. How to start?

How to solve these functional equations $f(x) = 1 + f(x) + f(x^2) + \ldots $ and $f(x) = 1 + f(x) + \big(f(x^2)\big)^2 + \ldots $?

$g(g(n)) = d(n)$ for all $n \in \mathbb{N}^*$

All functions that satisfy $f(x)^n = f(x^n)$

second derivative of a function equals a power of said function

How to solve $F(z,q) = q + z F(z,q) + z^2 \big( F(z,q^2) \big)^2$?

Functional Square Root Grapher

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