Question

Using continued fraction convergents to find a formula in terms of derivatives

score 258 · Answer 1 · 2017-04-09 03:51:12

258

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Using continued fraction convergents to find a formula in terms of derivatives

Published on 09 Apr 2017 - 3:51

score 109 · Answer 2 · 2023-02-21 18:20:02

109

Views

How do you properly notate $\frac{1}{x+\frac{1}{x+\frac{1}{x+...}}}$?

Published on 21 Feb 2023 - 18:20

score 146 · Answer 3 · 2023-02-27 17:14:04

146

Views

Define $f\left(x\right) = \frac{x}{x + \frac{x}{x + \frac{x}{x + \frac{x}{x + \vdots}}}}$. What is $f'\left(x\right)$, the derivative?

Published on 27 Feb 2023 - 17:14

score 86 · Answer 4 · 2023-03-03 22:33:54

86

Views

Taylor Series and Continued Fractions

Published on 03 Mar 2023 - 22:33

score 54 · Answer 5 · 2026-03-26 14:42:52

54

Views

For Which $a$ In $[0,1]^n$ Is $\text{frac}(ta)$ Maximally Aperiodic

Published on 26 Mar 2026 - 14:42

score 55 · Answer 6 · 2023-03-11 11:35:23

55

Views

Negative continued fraction with maximal numerator

Published on 11 Mar 2023 - 11:35

score 311 · Answer 7 · 2023-03-12 10:23:47

311

Views

Showing that there exists infinitely many rational numbers $\frac{p}{q}$ satisfying $|x - p/q|\leq \frac{1}{q^{2+t}}$ for irrational $x$ and $t>0$

Published on 12 Mar 2023 - 10:23

score 102 · Answer 8 · 2023-03-16 18:23:09

102

Views

Continued fraction inequality with well know constant as $\pi$ and golden ratio.

Published on 16 Mar 2023 - 18:23

score 191 · Answer 9 · 2023-03-17 17:03:48

191

Views

How to explain it ? Difference between two continued fraction very small

Published on 17 Mar 2023 - 17:03

score 173 · Answer 10 · 2026-03-26 09:45:52

173

Views

Simplifying a complicated continued fraction expression.

Published on 26 Mar 2026 - 9:45

score 88 · Answer 11 · 2023-03-26 16:51:54

88

Views

Why does this infinite repeating fraction seem to be equal to 2 different values?

Published on 26 Mar 2023 - 16:51

score 82 · Answer 12 · 2023-04-05 21:36:54

82

Views

Why does this error of a continued fraction decrease by a lot for large entries?

Published on 05 Apr 2023 - 21:36

score 65 · Answer 13 · 2023-04-09 19:59:10

65

Views

Even number of left shifts of continued fraction and convergence to specific limit

Published on 09 Apr 2023 - 19:59

score 114 · Answer 14 · 2023-04-13 09:48:49

114

Views

Is there any progress in evaluating the Continued Fraction with squares?

Published on 13 Apr 2023 - 9:48

score 72 · Answer 15 · 2026-03-26 01:12:37

72

Views

$\lim_{n\to \infty}\frac{F_{n+1}^{k}}{F_{n}^{k}}=\lim_{n\to \infty}\frac{F_{n+k}}{F_n}=\phi^{k},$ true? for odd $k$'s?

Published on 26 Mar 2026 - 1:12

List Question

Using continued fraction convergents to find a formula in terms of derivatives

How do you properly notate $\frac{1}{x+\frac{1}{x+\frac{1}{x+...}}}$?

Define $f\left(x\right) = \frac{x}{x + \frac{x}{x + \frac{x}{x + \frac{x}{x + \vdots}}}}$. What is $f'\left(x\right)$, the derivative?

Taylor Series and Continued Fractions

For Which $a$ In $[0,1]^n$ Is $\text{frac}(ta)$ Maximally Aperiodic

Negative continued fraction with maximal numerator

Showing that there exists infinitely many rational numbers $\frac{p}{q}$ satisfying $|x - p/q|\leq \frac{1}{q^{2+t}}$ for irrational $x$ and $t>0$

Continued fraction inequality with well know constant as $\pi$ and golden ratio.

How to explain it ? Difference between two continued fraction very small

Simplifying a complicated continued fraction expression.

Why does this infinite repeating fraction seem to be equal to 2 different values?

Why does this error of a continued fraction decrease by a lot for large entries?

Even number of left shifts of continued fraction and convergence to specific limit

Is there any progress in evaluating the Continued Fraction with squares?

$\lim_{n\to \infty}\frac{F_{n+1}^{k}}{F_{n}^{k}}=\lim_{n\to \infty}\frac{F_{n+k}}{F_n}=\phi^{k},$ true? for odd $k$'s?

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