# Tagged Questions

A is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number.

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### Continued fraction manipulation

I have the following continued fraction $$\frac{1}{a_1x+}\;\;\frac{1}{b_1+}\;\;\frac{1}{a_2x+}\;\;\frac{1}{b_2}$$ The paper I am reading then converts this to the following continued z-fraction ...
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### Continued Fraction Algorithm for 113/50

The numbers $a_k$ can be found for $\frac{113}{50}$ by using a continued fraction algorithm. Note that $\frac{113}{50}$ is rational, and as a result it will have to terminate. Can anyone help me ...
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### Continued Fraction for Root 5 [duplicate]

How can I find the continued fraction expansion for the square root of 5. Do this without the use of a calculator and show all the steps.
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### continued fraction expansion for √7 [duplicate]

Can someone help me find the continued fraction expansion for $\sqrt{7}$ just like I did for below. For $\sqrt{3}$ I did this: I was given that $x = \sqrt{3} -1$ $x = \frac{1}{1+\frac{1}{2+x}}$ ...
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### continued fraction of the roots of $x^2 - \frac{53793390359}{1088391168}x + \frac{823543}{12230590464} = 0$

I would like to find the continued fraction expansion of the roots of: $$x^2 - \frac{53793390359}{1088391168}x + \frac{823543}{12230590464} = 0$$ Eq 1.6 from [1] What makes this problem so ...
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### continued fraction of $3 + 17\sqrt{3}$

On a computer, I tried to iterate the Euclidean algorithm on the number $3 + 17\sqrt{3}$ and here is what I got: \begin{array}{ccccrcrcrcr} 3 + 17\sqrt{3} &=& 32 &\cdot\;(& 1&+&...
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### Integral of a Continued Fraction

How might one go about evaluating the following integral $\int_{-\infty}^{\infty}\mathrm{K}_{j=0}^{\infty}(F_{j}e^{-x^2})dx$? Where$\mathrm{K}$ denotes a continued fraction and $F_j$ is the jth ...
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### Why are there no continued fraction representation for $\pi$ obeying mathematical rules?

There are several irrational numbers that can be represented with continued fraction such that a mathematical rule arises in this continued fraction. For example, the Euler number $e$ can be ...
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### Multiply all terms in continued fraction by a constant

I noticed that continued the fraction for $\sqrt{12}$ is $3;2,6,2,6,2,\ldots$ and the continued fraction for $\sqrt{7\times12}$ is $9;6,18,6,18,6,\ldots$ all the terms in the continued fraction are ...
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### Continued fraction to irrational number

Let $[1;\overline{2,1}$] be a continued fraction. I want to find the corresponding number. I know how to transform fractions of the form $[a;\overline{b}]$ but I am having a hard time here. Thank you.
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### Different types of transcendental numbers based on continued-fraction representation

I've been reading Wikipedia's article on continued fractions. A few examples are given for the continued-fraction representation of irrational numbers: $\sqrt{19}=[4;2,1,3,1,2,8,2,1,3,1,2,8,\dots]$ ...
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### How find this Continued fraction $[1,3,5,7,9,11,\cdots]$ value.

show this: $$\alpha=[1,3,5,7,9,11,\cdots]=1+\dfrac{1}{3+\dfrac{1}{5+\dfrac{1}{7+\dfrac{1}{\cdots}}}}=\dfrac{e^2+1}{e^2-1}$$ I found wiki Continued fraction also not have this problem,maybe this ...
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### Closed-form of infinite continued fraction involving factorials

Is there a closed form of this: $$1!+\dfrac{1}{2!+\dfrac{1}{3!+\dfrac{1}{4!+\ldots}}}$$