期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2009
卷号：2009
DOI：10.1155/2009/941920
出版社：Hindawi Publishing Corporation
摘要：We consider certain probability problems which are naturally related to
integer partitions. We show that the corresponding probabilities are values of classical
modular forms. Thanks to this connection, we then show that certain ratios of
probabilities are specializations of the Rogers-Ramanujan and Ramanujan- Selberg-
Gordon-Göllnitz continued fractions. One particular evaluation depends on a result
from Ramanujan's famous first letter to Hardy.
