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ON SOME NEW MODULAR RELATIONS FOR RAMANUJAN'S REMARKABLE PRODUCT OF THETA FUNCTIONS

M. S. MAHADEVA NAIKA|S. Chandankumar|B. HEMANTHKUMAR
장전수학회 (Jangjeon Mathematical Society)|2013.07|Advanced Studies in Contemporary Mathematics|제23권 제3호|pp. 431-448

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키워드

Modular equationsTheta-functionsRemarkable product of theta-functions.
주제분류수학

초록

In this paper, we establish several new P{Q mixed modular equations involving theta{ functions which are similar to those recorded by Ramanujan in his notebooks. As an application, we establish several new general formulas for explicit evaluations of Ramanujan's remarkable product of theta{functions and a remarkable product of theta{functions.

Abstract

In this paper, we establish several new P{Q mixed modular equations involving theta{ functions which are similar to those recorded by Ramanujan in his notebooks. As an application, we establish several new general formulas for explicit evaluations of Ramanujan's remarkable product of theta{functions and a remarkable product of theta{functions.

참고문헌 (17)

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  2. C. Adiga, "On Ramanujan’s cubic continued fraction and explicit evaluations of theta-functions", Indian J. Pure Appl. Math., 35(9), pp.1047~1062 (2004)
  3. B. C. Berndt, "Ramanujan’s Notebooks, Part III" (1991), Springer-Verlag
  4. B. C. Berndt, "Ramanujan’s Notebooks, Part IV" (1994), Springer-Verlag
  5. B. C. Berndt, "Ramanujan’s remarkable product of the theta-function", Proc. Edin- burgh Math. Soc., 40, pp.583~612 (1997)
  6. B. C. Berndt, "Ramanujan’s identities for eta-functions", Math. Ann., 292(1), pp.561~573 (1992)
  7. B. C. Berndt, "A new class of theta-function identities originating in Ramanujan’s notebooks", J. Number Theory, 48(2), pp.224~242 (1994)
  8. S. Bhargava, "A new class of modular equations in Ramanujan’s alternative theory of elliptic function of signature 4 and some new P –Q eta–function identities", Indian J. Math, 45(1), pp.23~39 (2003)
  9. S. Bhargava, "A new class of modular equations akin to Ramanujan’s P –Q eta–function identities and some evaluations there from", Adv. Stud. Contemp. Math, 5(1), pp.37~48 (2002)
  10. M. S. Mahadeva Naika, "P-Q eta function identities and computation of Ramanujan-Weber class invariants", J. Indian Math. Soc., 70(1-4), pp.121~134 (2003)
  11. M. S. Mahadeva Naika, "On some new general theorems for the explicit evaluations of Ramanujan’s remarkable product of theta-function", The Ramanujan J, 15(3), pp.349~366 (2008)
  12. M. S. M. Naika, "On some new modular equations of degree 9 and their applications", Advanced Studies in Contemporary Mathematics, 22(1), pp.99~115 (2012), 장전수학회
  13. M. S. Mahadeva Naika, "Modular equations for the ratios of Ramanujan’s theta function ψ and evaluations", New Zealand J. Math, 40, pp.33~48 (2010)
  14. M. S. M. Naika, "Explicit evaluations of Ramanujan's remarkable product of theta-function", Advanced Studies in Contemporary Mathematics, 13(2), pp.235~254 (2006), 장전수학회
  15. M. S. Mahadeva Naika, "On some remarkable product of theta-function", Aust. J. Math. Anal. Appl., 5(1), pp.1~15 (2008)
  16. S. Ramanujan, "Notebooks (2 volumes)" (1957), Tata Institute of Fundamental Research
  17. S. Ramanujan, "The lost notebook and other unpublished papers" (1988), Narosa

관련 논문AI추천

CERTAIN 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 some new modular equations of degree 9 and their applicationsM. Manjunatha, M. S. M. Naika, S. Chandankumar장전수학회 · Advanced Studies in Contemporary Mathematics2012 · 제22권 제1호ON SOME P-Q MIXED MODULAR EQUATIONS OF DEGREE 5M. Harish, M. S. MAHADEVA NAIKA, S. Chandankumar장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2020 · 제23권 제3호New identities for ratios of Ramanujan’s theta functionK. Sushan Bairy, M. S. MAHADEVA NAIKA, S. Chandankumar장전수학회 · Advanced Studies in Contemporary Mathematics2017 · 제27권 제1호New ramanujan’s remarkable product of Theta-function and their explicit evaluationsB. N. DHARMENDRA장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2019 · 제22권 제4호Some 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 제3호

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