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

N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

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

VL - 355

SP - 2397

EP - 2411

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 6

ER -