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The Australian Journal of Mathematical Analysis and Applications
ISSN 1449-5910 |
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Paper's Title:
On Some Remarkable Product of Theta-function
Author(s):
M. S. Mahadeva Naika, M. C. Maheshkumar and K. Sushan Bairy
Department of Mathematics,
Bangalore University, Central College Campus,
Bangalore-560 001,
INDIA
msmnaika@rediffmail.com
softmahe@rediffmail.com
ksbairy@gmail.com
Abstract:
On pages 338 and 339 in his first notebook, Ramanujan records
eighteen values for a certain product of theta-function. All these
have been proved by B. C. Berndt, H. H. Chan and L-C. Zhang
[4]. Recently M. S. Mahadeva Naika and B. N. Dharmendra
[7,
8] and Mahadeva Naika and M. C. Maheshkumar
[9] have obtained general theorems to establish explicit
evaluations of Ramanujan's remarkable product of theta-function.
Following Ramanujan we define a new function bM,N as
defined in (1.5). The main purpose of this paper is to
establish some new general theorems for explicit evaluations of
product of theta-function.
Paper's Title:
Some Identities for Ramanujan - Göllnitz - Gordon Continued fraction
Author(s):
M. S. Mahadeva Naika, B. N. Dharmendra and S. Chandan Kumar
Department of Mathematics,
Bangalore University,
Central College Campus,
Bangalore-560 001,
INDIA
Department of Mathematics,
Maharani's Science College for Women,
J. L. B. Road, Mysore-570 001,
INDIA
Abstract:
In this paper, we obtain certain P--Q eta--function identities, using which we establish identities providing modular relations between Ramanujan-Göllnitz-Gordon continued fraction H(q) and H(q^n) for n= 2, 3, 4, 5, 7, 8, 9, 11, 13, 15, 17, 19, 23, 25, 29 and 55.
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