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Some modular relations for the Roger-Ramanujan type functions of order six and its applications to partitions

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Some modular relations for the Roger-Ramanujan type functionsof order six and its applications to partitions

Abstract

Some modular relations for the Roger-Ramanujan type functionsof order six and its applications to partitions

참고문헌 (17)

  1. C. Adiga, "Chapter 16 of Ramanujan's second notebook: Theta functions and q-series", Mem. Amer. Math. Soc., 315, pp.1~91 (1985)
  2. C. Adiga, "Some new modular relations for the cubic functions", South East Asian Bull. Math., 36, pp.1~19 (2012)
  3. G. E. Andrews, "An Introduction to Ramanujan's \Lost" Notebook", Amer. Math. Monthly, 86, pp.89~108 (1976)
  4. B. C. Berndt, "Ramanujan's Notebooks, Part III" (1991), Springer-Verlag
  5. B. C. Berndt, "Ramanujan's forty identities for the Rogers-Ramanujan functions", Mem. Amer. Math. Soc., 188(880), pp.1~96 (2007)
  6. A. J. F. Biagioli, "A proof of some identities of Ramanujan using modular functions", Glasgow. Math. J., 31, pp.271~295 (1989)
  7. D. Bressoud, "Proof and generalization of certain identities conjectured by Ramanujan", Ph.D., pp.1977
  8. D. Hickerson, "A proof of the mock theta conjectures", Invent. Math, 94, pp.639~660 (1988)
  9. S. Ramanujan, "Proof of certain identities in combinatory analysis", Proc. Cambridge Philos. Soc., 19, pp.214~216 (1919)
  10. S. Ramanujan, "Algebraic relations between certain in nite products", Proc. Lond. Math. Soc, 2 (1920)
  11. S. Ramanujan, "Collected Papers" (1927), Cambridge University Press
  12. L. J. Rogers, "Second memoir on the expansion of certain in nite products", Proc. London Math. Soc., 25, pp.318~343 (1894)
  13. L. J. Rogers, "On a type of modular relation", Proc. London Math. Soc., 19(2), pp.387~397 (1921)
  14. L. J. Slater, "Further identities of Rogers-Ramanujan type", London Math. Soc., 54(2), pp.147~167 (1952)
  15. K. R. Vasuki, "Two modular equations for squares of the cubic-functions with applications", Note di Mathematica, 30, pp.61~70 (2010)
  16. G. N.Watson, "Proof of certain identities in combinatory analysis", J. Indian Math. Soc., 20, pp.57~69 (1933)
  17. H. Yesilyurt, "A generalization of a modular identity of Rogers", J. Number Thy., 129, pp.1256~1271 (2009)

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