Śleszyński–Pringsheim theorem
id:
leszy-ski-pringsheim-theorem-284-7139372
title:
Śleszyński–Pringsheim theorem
text:
In mathematics, the Śleszyński–Pringsheim theorem is a statement about convergence of certain continued fractions. It was discovered by Ivan Śleszyński and Alfred Pringsheim in the late 19th century. It states that if a n , b n , for n = 1 , 2 , 3 , … are real numbers and | b n | ≥ | a n | + 1 for all n , then converges absolutely to a number f satisfying 0 < | f | < 1 , meaning that the series where A n / B n are the convergents of the continued fraction, converges absolutely.
brand slug:
wiki
category slug:
encyclopedia
description:
Criterion for convergence of continued fractions
original url:
https://en.wikipedia.org/wiki/%C5%9Aleszy%C5%84ski%E2%80%93Pringsheim_theorem
date created:
date modified:
2023-07-24T11:20:54Z
main entity:
{"identifier":"Q8081891","url":"https://www.wikidata.org/entity/Q8081891"}
image:
fields total:
13
integrity:
14