# Tagged Questions

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### Approximating $\frac{t^2}{3-\frac{t^2}{5-\frac{t^2}{7-\frac{t^2}{9-\cdots}}}}$

What is a good approximation for $$\omega=\frac{t^2}{3-\frac{t^2}{5-\frac{t^2}{7-\frac{t^2}{9-\cdots}}}}$$ This will be used to find $$T=\frac{t}{1-\omega}$$ Without using Lambert's continued fraction ...
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I have two numbers, $A$ and $B$, that are sums of integer multiples of a set of square roots of small primes (and 1) and their products: $A = a_0 + a_1\sqrt 2 + a_2\sqrt 3 + a_3\sqrt 5 + a_4\sqrt 6 + ... 2answers 192 views ### Continued Fractions Approximation I have come across continued fractions approximation but I am unsure what the steps are. For example How would you express the following rational function in continued-fraction form:$${x^2+3x+2 ... 1answer 996 views ### Approximating$\arctan x$for large$|x|$I would like to know if there is reasonably fast converging method for computing large arguments of arctan. Until now I've came across Taylor series that converges only on interval$(-1,1)$and for ... 0answers 76 views ### Is that observation really a property of the log of coefficients of continued fractions (example: cf(log(3)/log(2)) I'm again looking at the problem of approximation of perfect powers of 2 to that of 3 (I assume$\small q_N = 2^S / 3^N \gt 1 $) and specifically using the continued fraction representation of$\small ...
Given two nonzero real numbers $x$ and $y$ such that $y/x$ is irrational, a real number $z$ to be approximated, and a tolerance $\epsilon$, give me an algorithm that will provide coprime integers $a$ ...