@inbook{a8ce59e89b314012af5d17daca395892,

title = "On the Generalized Rogers-Ramanujan Continued Fraction",

abstract = "On page 26 in his lost notebook, Ramanujan states an asymptotic formula for the generalized Rogers-Ramanujan continued fraction. This formula is proved and made slightly more precise. A second primary goal is to prove another continued fraction representation for the Rogers-Ramanujan continued fraction conjectured by R. Blecksmith and J. Brillhart. Two further entries in the lost notebook are examined. One of them is an identity bearing a superficial resemblance to the generating function for the generalized Rogers-Ramanujan continued fraction. Thus, our third main goal is to establish, with the help of an idea of E Franklin, a partition bijection to prove this identity.",

keywords = "Rogers-Ramanujan continued fraction, Ramanujan{\textquoteright}s lost notebook, Franklin{\textquoteright}s involution, generalized Rogers-Ramanujan continued fraction",

author = "Berndt, {Bruce C.} and Yee, {Ae Ja}",

year = "2003",

doi = "10.1007/978-1-4757-6044-6_23",

language = "English (US)",

isbn = "978-1-4020-7615-2",

series = "Developments in Mathematics",

publisher = "Springer",

pages = "321--331",

editor = "Bruce Berndt and Ken Ono",

booktitle = "Number Theory and Modular Forms",

address = "Germany",

}