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

• Autorzy: Soon-Yi Kang
• Języki publikacji: EN

Kategorie tematyczne

• 40A15: Convergence and divergence of continued fractions
• 11F27: Theta series; Weil representation; theta correspondences

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 90
• Numer: 1
• Strony: 49-68

Daty

wydano

1999

otrzymano

1998-06-19

poprawiono

1998-12-08

Twórcy

autor

Soon-Yi Kang

• 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.