An Introduction to Ramanujan's "lost" Notebook

1979 ◽  
Vol 86 (2) ◽  
pp. 89 ◽  
Author(s):  
George E. Andrews
Keyword(s):  
Lost Notebook ◽  
Ramanujan's Lost Notebook

scholarly journals Ramanujan's “Lost” Notebook. I. Partial θ-functions

1981 ◽  
Vol 41 (2) ◽  
pp. 137-172 ◽  
Author(s):  
George E Andrews
Keyword(s):  
Lost Notebook ◽  
Ramanujan's Lost Notebook

The final problem: an identity from Ramanujan's lost notebook

2019 ◽  
Vol 100 (2) ◽  
pp. 568-591 ◽  
Author(s):  
Bruce C. Berndt ◽  
Junxian Li ◽  
Alexandru Zaharescu
Keyword(s):  
Lost Notebook ◽  
Ramanujan's Lost Notebook

Simplicity and Surprise in Ramanujan's “Lost” Notebook

1997 ◽  
Vol 104 (10) ◽  
pp. 918-925
Author(s):  
George E. Andrews
Keyword(s):  
Lost Notebook ◽  
Ramanujan's Lost Notebook

FOUR IDENTITIES FOR THIRD ORDER MOCK THETA FUNCTIONS

2018 ◽  
Vol 239 ◽  
pp. 173-204 ◽  
Author(s):  
GEORGE E. ANDREWS ◽  
BRUCE C. BERNDT ◽  
SONG HENG CHAN ◽  
SUN KIM ◽  
AMITA MALIK
Keyword(s):  
Generating Functions ◽  
Theta Functions ◽  
Mock Theta Functions ◽  
Third Order ◽  
Lost Notebook ◽  
Ramanujan's Lost Notebook

In 2005, using a famous lemma of Atkin and Swinnerton-Dyer (Some properties of partitions, Proc. Lond. Math. Soc. (3) 4 (1954), 84–106), Yesilyurt (Four identities related to third order mock theta functions in Ramanujan’s lost notebook, Adv. Math. 190 (2005), 278–299) proved four identities for third order mock theta functions found on pages 2 and 17 in Ramanujan’s lost notebook. The primary purpose of this paper is to offer new proofs in the spirit of what Ramanujan might have given in the hope that a better understanding of the identities might be gained. Third order mock theta functions are intimately connected with ranks of partitions. We prove new dissections for two rank generating functions, which are keys to our proof of the fourth, and the most difficult, of Ramanujan’s identities. In the last section of this paper, we establish new relations for ranks arising from our dissections of rank generating functions.

Some Continued Fractions in Ramanujan’s Lost Notebook

2005 ◽  
Vol 146 (1) ◽  
pp. 37-48 ◽  
Author(s):  
Jongsil Lee ◽  
Jaebum Sohn
Keyword(s):  
Continued Fractions ◽  
Lost Notebook ◽  
Ramanujan's Lost Notebook

scholarly journals The continuous symmetric Hahn polynomials found in Ramanujan's lost notebook

2005 ◽  
Vol 307 (1) ◽  
pp. 153-166 ◽  
Author(s):  
Soon-Yi Kang ◽  
Sung-Geun Lim ◽  
Jaebum Sohn
Keyword(s):  
Hahn Polynomials ◽  
Lost Notebook ◽  
Ramanujan's Lost Notebook

scholarly journals Ramanujan's “Lost” Notebook VI: The mock theta conjectures

1989 ◽  
Vol 73 (2) ◽  
pp. 242-255 ◽  
Author(s):  
George E Andrews ◽  
F.G Garvan
Keyword(s):  
Lost Notebook ◽  
Ramanujan's Lost Notebook

“Algebraical oddities” in Ramanujan’s lost notebook

2012 ◽  
Vol 29 (1-3) ◽  
pp. 69-77 ◽  
Author(s):  
Michael D. Hirschhorn
Keyword(s):  
Lost Notebook ◽  
Ramanujan's Lost Notebook
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