The aim of research is to obtain new estimates of extent of irrationality for values \(\arctan \frac{1}{5}, \arctan\frac{1}{3}.\) In this article, we constructed a new integral for getting an irrationality measure of \(\arctan \frac{1}{5}\) based on the idea from work of K. Wu, 2002. We investigated the linear form generated by this integral and found that it allows to get a better estimate for this value. By the same method, we constructed an integral for obtaining an estimate of irrationality measure for \(\arctan \frac{1}{3},\) and we also got a new result for this value.

中文翻译：

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$ \ operatorname {arctg} \ frac {1} {n} $某些值的非理性测度

研究的目的是获得值\（\ arctan \ frac {1} {5}，\ arctan \ frac {1} {3}。\}的非理性程度的新估计。在本文中，我们构造了一个新的积分基于K. Wu，2002年的思想，得到\（\ arctan \ frac {1} {5} \）的非理性度量。我们研究了由该积分生成的线性形式，发现它可以得到一个更好地估计该值。通过相同的方法，我们构造了一个积分，以获取\（\ arctan \ frac {1} {3}，\）的非理性测度的估计，并且我们也获得了该值的新结果。