# Questions tagged [continued-fractions]

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### Problem with "OverBar"

In my equation, I would like to add a bar to the second fraction, but the "OverBar" does not work. I would appreciate it if you could tell me what the ...
73 views

### Computing symbolic continued fractions for rational functions with respect to a variable

There are quite a few questions here about continued fractions, so this might be a duplicate, but I honestly could not find what I want. What I want is, having two polynomials ...
• 2,066
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### How can I prove that the sequence converges to $\log(2)$?

There are two rational sequences. One of them describes convergents of the continued fraction for $\log(2)$. Its Mathematica code is as follows: ...
• 51
1 vote
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### Transform a continued fraction to an ordinary fraction

I need to calculate (tranform to a 1-level fraction) the following continued fraction: ...
• 11
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### Evaluate the following simple continued fractions

A continued fraction is a fraction whose numerator is an integer and whose denominator is an integer added to a fraction whose numerator is an integer and whose denominator is an integer added to a ...
60 views

### Is it possible to display numbers in the form of infinitely repeating decimal fractions $0. \bar{1}$ as ticks in a plot?

I want to show the infinitely repeating decimal fractions in these explicit forms $0. \bar{1}$ and $0. \bar{2}$ as Thicks in a plot; is it possible to do that? If ...
• 749
101 views

Found this one in closed forms of a fraction. Wolfram only gives a way to copy as plain text: (3830 W_Wad)/1177≈0.97621070518266779949 And then it won't recognise ...
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### Representing a general continued fraction in a list for ContinuedFraction

The initial mathematical problem is to solve for $x$ in: $$x = \sqrt{19} + \frac{91}{\sqrt{19} + \frac{91}{\sqrt{19} + \frac{91}{\sqrt{19} + \frac{91}{\sqrt{19} + \frac{91}{x}}}}}$$ (Notice the $x$ in ...
• 41.2k
101 views

### How to implement statistics for the length of continued fractions of a result on MATHEMATICA

After successfully generating the reduced fraction of two coprime in interval (0,1] with the following; ...
122 views

### Deriving formulas for continued fraction expansions

A version of a continued fraction expansion of a rational number $r\in \mathbb Q$ is defined as \begin{align} r =[a_0,a_1,a_2,\ldots,a_k]= a_0 - \frac{1}{a_1 - \frac{1}{a_2 - \dots - \tfrac{1}{a_k}}} \...
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### Simplify multiple layers fractions

I have a complicated fraction ...
71 views

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### How to calculate this function

Please, I would like to calculate this function which contains an infinite continued fraction ...
• 51
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### Understanding FromContinuedFraction

In the detail section of the documentation page for FromContinuedFraction we read that: FromContinuedFraction[{a1,a2,…,{b1,b2,…}}] returns the exact number whose ...
• 6,687
1 vote
420 views

### Writing code to produce continued fractions

I have been trying to create a continuing fraction to help prove the theory about any rational number: a/b being able to be written as a continued fraction where the remainders found in the Euclidean ...
1 vote
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### Gauss Continued Fraction for Hypergeometric Functions

I would like to calculate the Gauss Continued Fraction for this particular Hypergeometric function: _{2}F_{1}\left( 1-\frac{1}{p}, \frac{1}{p}; 1+\frac{1}{p}; x^p \right) \end{...
• 737
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### Using Mathematica to find an alternative continued fraction for $\zeta(5)$

Given the Riemann zeta function $\zeta(n)$. I. $x=\zeta(3)$ Using Euler's continued fraction formula, we can form $\zeta(3)$'s cfrac as, Ax+B = \cfrac{1}{v_1 - \cfrac{1^6}{v_2 - \cfrac{2^6}{...
484 views

### Truncate an infinite continued fraction at order 2000

I want to solve an equation which contains an infinite continued fraction $F(n)$. Then I must (obviously) truncate this continued fraction at $n=2000$. The problem here is that Mathematica does not ...
• 31
The $n^{\text{th}}$ negative continued fraction convergent $x_n$ of a positive real $x$ is computed by the nested function \begin{align} x_n = k_1 - \frac{1}{k_2 - \frac{1}{k_3 - \dots - \tfrac{1}{k_n}...