SOME VALUES FOR THE ROGERS-RAMANUJAN CONTINUED-FRACTION

被引：26
作者：
BERNDT, BC
CHAN, HH
机构：
来源：
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 1995年 / 47卷 / 05期
关键词：
D O I：
10.4153/CJM-1995-046-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In his first and lost notebooks, Ramanujan recorded several values for the Rogers-Ramanujan continued fraction. Some of these results have been proved by K. G. Ramanathan, using mostly ideas with which Ramanujan was unfamiliar. In this paper, eight of Ramanujan's values are established; four are proved for the first time, while the remaining four had been previously proved by Ramanathan by entirely different methods. Our proofs employ some of Ramanujan's beautiful eta-function identities, which have not been heretofore used for evaluating continued fractions.
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页码：897 / 914
页数：18
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