On Irrationality Measure of Some Values of $\operatorname{arctg} \frac{1}{n}$

Autor:	M. G. Bashmakova, V. Kh. Salikhov
Rok vydání:	2020
Předmět:	010101 applied mathematics Discrete mathematics General Mathematics Linear form Mathematics::History and Overview 010102 general mathematics Irrationality Inverse trigonometric functions 0101 mathematics 01 natural sciences Value (mathematics) Measure (mathematics) Mathematics
Zdroj:	Russian Mathematics. 64:29-37
ISSN:	1934-810X 1066-369X
DOI:	10.3103/s1066369x2012004x
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::7d10450a84e74c285c3fb17fe70c91bf https://doi.org/10.3103/s1066369x2012004x Zobrazit plný text záznamu Full text from SpringerLink