논문KCI 등재
Explicit evaluations of Ramanujan's remarkable product of theta-function
1
조회
0
다운로드
6
인용
0
참고문헌
주제분류수학
초록
Abstract
On pages 338 and 339 in his first notebook [9], Ramanujan records eighteen values for a certain product of theta-function. All these have been proved by B. C. Berndt,H. Chan and L-C. Zhang [7]. The main purpose of this paper is to establish several new explicit evaluations of Ramanujan’s remarkable product of theta-function.
참고문헌 (9)
- Adiga, C., "Chapter 16 of Ramanujan’s second notebook: Theta-function and q-series", Mem. Amer. Math. Soc., 53(315) (1985), Amer. Math. Soc., Providence
- Berndt, B. C., "Ramanujan’s Notebooks, Part III" (1991), Springer-Verlag, New York
- Berndt, B. C., "Ramanujan’s Notebooks, Part IV" (1994), Springer-Verlag, New York
- Berndt, B. C., "Ramanujan’s Notebooks, Part V" (1998), Springer-Verlag, New York
- Berndt, B. C., "Ramanujan’s remarkable product of the theta-function", Proc. Edinburgh Math. soc., 40, pp.583~612 (1997)
- Borwein, J. M., "Pi and AGM" (1987), Wiley, New York
- Naika, M. S. Mahadeva, "P −Q eta-function identities and computations of Ramanujan-Weber class invariants", The J. Indian Math. soc., 70 (2003)
- Naika, M. S. Mahadeva, "On some new general theorems for the explicit evaluations of Ramanujan’s remarkable product of theta-function", The Ramanujan Journal
- Ramanujan, S., "Notebooks, 2 volumes" (1957), Tata Institute of Fundamental Research, Bombay
관련 논문AI추천
Some Result on Analogous to Ramanujan’s Remarkable Product of Theta FunctionB. N. DHARMENDRA, R. Raghavendra장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2020 · 제23권 제3호ON SOME NEW MODULAR RELATIONS FOR RAMANUJAN'S REMARKABLE PRODUCT OF THETA FUNCTIONSB. HEMANTHKUMAR, M. S. MAHADEVA NAIKA, S. Chandankumar장전수학회 · Advanced Studies in Contemporary Mathematics2013 · 제23권 제3호New ramanujan’s remarkable product of Theta-function and their explicit evaluationsB. N. DHARMENDRA장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2019 · 제22권 제4호On some new modular equations of degree 9 and their applicationsM. Manjunatha, M. S. M. Naika, S. Chandankumar장전수학회 · Advanced Studies in Contemporary Mathematics2012 · 제22권 제1호CERTAIN MODULAR RELATIONS FOR REMARKABLE PRODUCT OF THETA-FUNCTIONSK. Sushan Bairy, M. S. MAHADEVA NAIKA, N. P. SUMAN장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2014 · 제17권 제3호On the infinite products derived from theta series I구자경, 김대열대한수학회 · 대한수학회지2007 · 제44권 제1호
이 간행물의 다른 논문 (10건)
Ward's “calculus of sequences”, q-calculus and the limit q->-1M. Schorkpp. 131-141Van der Waerden's continuity theorem for the commutator subgroups of connected Lie groups and Mishchenko's conjectureA. I. Shternpp. 143-158A note on the alternating sums of powers of consecutive q-integersS.-H. Rim, T. Kim, Y. Simsekpp. 159-164The weighted Heron dual mean in variablesZh.-H. Zhang, V. Lokeshapp. 165-170On colorings of strongly multiplicative and strongly quotient graphsR .K. Zaferani, C. Adigapp. 171-182
