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Results tagged with real-analysis
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user 116428
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
1
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0
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Can Carlsons's iterative algorithm for $\arctan x$ be inverted to get one for $\tan x$?
In the article An algorithm for computing logarithms and arctangents, by B. C. Carlson, the following iterative algorithm for arctangents is given:
The algorithm uses that $2^n\tan(2^{-n}\arctan(x) …
- 2,784
2
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0
answers
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Is there an infinite product like this for $\cos x$?
There are infinite products of iterated square roots for $\log x$ and $\arccos x$ as functions of $x$. For example
$$\log x = \frac{x - 1}{\sqrt{x}\sqrt{\frac{1}{2} + \frac{1}{2}\left ( \frac{1 + x}{ …
- 2,784
4
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0
answers
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Is there any closed form expression for $\sum_{k=2}^\infty(-1)^k \left(- \frac{1}{2}\right)^...
Is there any closed form expression for the following serie?
$$\sum_{k=2}^\infty(-1)^k \left(- \frac{1}{2}\right)^{\frac{k(k+1)}{2}}$$
Or at least a proof that it is an irrational number. The contex …
