PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
1999 | 90 | 1 | 49-68
Tytuł artykułu

Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
90
Numer
1
Strony
49-68
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-06-19
poprawiono
1998-12-08
Twórcy
autor
  • Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801, U.S.A.
Bibliografia
  • [1] G. E. Andrews, B. C. Berndt, L. Jacobsen and R. L. Lamphere, The Continued Fractions Found in the Unorganized Portions of Ramanujan's Notebooks, Mem. Amer. Math. Soc. 477 (1992).
  • [2] B. C. Berndt, Ramanujan's Notebooks, Part III, Springer, New York, 1991.
  • [3] B. C. Berndt, Ramanujan's Notebooks, Part IV, Springer, New York, 1994.
  • [4] B. C. Berndt, Ramanujan's Notebooks, Part V, Springer, New York, 1997.
  • [5] B. C. Berndt and H. H. Chan, Ramanujan's explicit values for the classical theta-function, Mathematika 42 (1995), 278-294.
  • [6] B. C. Berndt and H. H. Chan, Some values for the Rogers-Ramanujan continued fraction, Canad. J. Math. 47 (1995), 897-914.
  • [7] B. C. Berndt, H. H. Chan and L.-C. Zhang, Explicit evaluations of the Rogers-Ramanujan continued fraction, J. Reine Angew. Math. 480 (1996), 141-159.
  • [8] H. H. Chan, On Ramanujan's cubic continued fraction, Acta Arith. 73 (1995), 343-355.
  • [9] S.-Y. Kang, Some theorems on the Rogers-Ramanujan continued fraction and associated theta functions in Ramanujan's lost notebook, Ramanujan J. 3 (1999), 91-111.
  • [10] K. G. Ramanathan, On Ramanujan's continued fraction, Acta Arith. 43 (1984), 209-226.
  • [11] K. G. Ramanathan, On the Rogers-Ramanujan continued fraction, Proc. Indian Acad. Sci. Math. Sci. 93 (1984), 67-77.
  • [12] K. G. Ramanathan, Ramanujan's continued fraction, Indian J. Pure Appl. Math. 16 (1985), 695-724.
  • [13] K. G. Ramanathan, Some applications of Kronecker's limit formula, J. Indian Math. Soc. 52 (1987), 71-89.
  • [14] K. G. Ramanathan, On some theorems stated by Ramanujan, in: Number Theory and Related Topics, Tata Inst. Fund. Res. Stud. Math. 12, Oxford Univ. Press, Bombay, 1989, 151-160.
  • [15] S. Ramanujan, Notebooks (2 volumes), Tata Inst. Fund. Res., Bombay, 1957.
  • [16] S. Ramanujan, Collected Papers, Chelsea, New York, 1962.
  • [17] S. Ramanujan, Modular equations and approximations to π, Quart. J. Math. (Oxford) 45 (1914), 350-372.
  • [18] S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988.
  • [19] L. J. Rogers, Second memoir on the expansion of certain infinite products, Proc. London Math. Soc. 25 (1894), 318-343.
  • [20] G. N. Watson, Theorems stated by Ramanujan ( VII): Theorems on continued fractions, J. London Math. Soc. 4 (1929), 39-48.
  • [21] G. N. Watson, Theorems stated by Ramanujan (IX): Two continued fractions, J. London Math. Soc. 4 (1929), 231-237.
  • [22] H. Weber, Lehrbuch der Algebra, dritter Band, Chelsea, New York, 1961.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav90i1p49bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.