TY - JOUR
T1 - On Ramanujan's continued fraction for (q2;q3) ∞(q; q3)∞
AU - Andrews, George E.
AU - Berndt, Bruce C.
AU - Sohn, Jaebum
AU - Yee, Ae Ja
AU - Zaharescu, Alexandru
PY - 2003/6
Y1 - 2003/6
N2 - The continued fraction in the title is perhaps the deepest of Ramanujan's q-continued fractions. We give a new proof of this continued fraction, more elementary and shorter than the only known proof by Andrews, Berndt, Jacobsen, and Lamphere. On page 45 in his lost notebook, Ramanujan states an asymptotic formula for a continued fraction generalizing that in the title. The second main goal of this paper is to prove this asymptotic formula.
AB - The continued fraction in the title is perhaps the deepest of Ramanujan's q-continued fractions. We give a new proof of this continued fraction, more elementary and shorter than the only known proof by Andrews, Berndt, Jacobsen, and Lamphere. On page 45 in his lost notebook, Ramanujan states an asymptotic formula for a continued fraction generalizing that in the title. The second main goal of this paper is to prove this asymptotic formula.
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U2 - 10.1090/S0002-9947-02-03155-0
DO - 10.1090/S0002-9947-02-03155-0
M3 - Article
AN - SCOPUS:0037693039
SN - 0002-9947
VL - 355
SP - 2397
EP - 2411
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 6
ER -