Open AccessSequence transformations in proofs of irrationality of some fundamental constants
Author(s) -
В. П. Варин
Publication year - 2021
Publication title -
preprint/preprinty ipm im. m.v. keldyša
Language(s) - English
Resource type - Journals
eISSN - 2071-2901
pISSN - 2071-2898
DOI - 10.20948/prepr-2021-84
Subject(s) - irrationality , mathematical proof , convergence (economics) , mathematics , sequence (biology) , acceleration , transformation (genetics) , rate of convergence , constant (computer programming) , calculus (dental) , computer science , rationality , epistemology , classical mechanics , key (lock) , geometry , philosophy , computer security , dentistry , economic growth , chemistry , biology , genetics , biochemistry , programming language , medicine , physics , economics , gene
Transformation of number sequences (convergence acceleration) is one of the classical chapters of numerical analysis. These algorithms are used both for solution of practical problems and for the development of more advanced numerical methods. At the same time, numerical methods have found numerous applications in the number theory. One of the classical problems of number theory is the proof of irrationality of some fundamental constants, where the high rate of convergence of sequences of rational numbers plays a crucial role. However, as far as we know, the applications of (classical) convergence acceleration algorithms to the proofs of irrationality do not exist. This study is an attempt to fill this gap and to draw attention to this direction of research.