TY - JOUR
T1 - Some theorems on the ro gers-ramanujan continued fraction in Ramanujan's lost notebook
AU - Berndt, Bruce C.
AU - Huang, Sen Shan
AU - Sohn, Jaebum
AU - Son, Seung Hwan
PY - 2000
Y1 - 2000
N2 - In his first two letters to G. H. Hardy and in his notebooks, Ramanujan recorded many theorems about the Rogers-Ramanujan continued fraction. In his lost notebook, he offered several further assertions. The purpose of this paper is to provide proofs for many of the claims about the RogersRamanujan and generalized Rogers-Ramanujan continued fractions found in the lost notebook. These theorems involve, among other things, modular equations, transformations, zeros, and class invariants.
AB - In his first two letters to G. H. Hardy and in his notebooks, Ramanujan recorded many theorems about the Rogers-Ramanujan continued fraction. In his lost notebook, he offered several further assertions. The purpose of this paper is to provide proofs for many of the claims about the RogersRamanujan and generalized Rogers-Ramanujan continued fractions found in the lost notebook. These theorems involve, among other things, modular equations, transformations, zeros, and class invariants.
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U2 - 10.1090/s0002-9947-00-02337-0
DO - 10.1090/s0002-9947-00-02337-0
M3 - Article
AN - SCOPUS:23044520241
SN - 0002-9947
VL - 352
SP - 2157
EP - 2177
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 5
ER -